When J and K first encounter Boris on the rooftop of Wu's restaurant, Boris forces them off the roof, hanging on a door. When J and K hit the ground, there is a brief shot showing them falling in opposite directions. However, the very next shot shows them on the ground, side by side.
The Apollo 11 launch site is referred to as Cape Canaveral. While this would have been natural for Agent J, it would have been unnatural for young Agent K as the Cape was re-named Cape Kennedy after President John F. Kennedy's assassination in 1963. The name only reverted back to Cape Canaveral in 1973, way after Apollo 11 was launched.
The Spanish flag flapping in the wind during the Cape Canaveral launch scene is the current Spanish flag. In 1969, Spain - under the Francisco Franco regime, had a different flag (bearing a coat of arms with a black eagle).
The 1969 cops wear light powder blue shirts introduced in 1973. The correct uniform would have been dark navy blue shirts without NYPD patches on the sleeves, which were not designed as the department emblem until 1973 as well.
Also during the Andy Warhol party there are lights seen on the stage curtains, commonly called a Star Cloth or Curtain today. This technology as displayed in the film did not exist in 1969, in fact any sort of mass production of very low powered Red LEDs only started in 1968 and prior to that most LEDs cost in the vicinity of $200 each!. White LEDs did not exist then.
The slidewire astronaut escape baskets were not installed until after the Apollo era, and were used for the Space Shuttle. Apollo astronauts were expected to descend in a fast elevator, then retreat to a bunker under the pad in case of emergency.
During the Andy Warhol party scene the stage curtains are supported by an aluminum truss structure. In 1969 this type of system did not exist and any truss from that era would have been made from steel.
In 1969 every baseball cap had a green underbill. In the film you can see a 1969 Mets pitcher using a gray underbill cap. Gray underbill caps aren't introduced until 1994. In 2007 this color was dropped in favor of the current black.
When J, K and Griffin enter MIB headquarters at the Brooklyn-Battery Tunnel ventilation building to fly to Cape Canaveral, the tilting shot prominently features three medallions over the entrance doors. Those cast aluminum reliefs, designed by Paul Manship, would not have been over the building entrance in 1969. They would have been mounted on the New York Coliseum convention center in midtown Manhattan. The reliefs were removed from the Coliseum in 1999 as it was being prepared for demolition and only later mounted on the ventilation building.
The Colonel wears a brown belt with a brown holster. In 1956 the US Army officially changed the color for belts, holsters, and shoes from Cafe Brown to Black. In 1969 the Colonel should have a black holster, and belt like the M.P.s are wearing.
In 1969, we saw two versions of the neuralizer. The first was used at MIB when K was trying to nerualize J, rolling him into a gigantic version, but, later on, K had a portable one with battery power that he used on James. So why did they need the huge version if the portable version worked as well as it did?
After Boris shoots his spears at J, he jumps Boris and himself off the roof and goes back in time a minute to avoid being shot with the spears. When the spears miss him he says "Right! Left! Left! Right!" but his mouth is out-of-sync when saying "Left! Left!".
When Jeffrey Price asks J what is the plan, J replies "You're going to send me back to July 15, 1969." Two shots are shown as he says this line. The first shot shows a reverse angle of J starting to speak the line, however, his jaw is never shown moving. This line would require his jaw to move.
Griffin states about the New York Mets saying "They were in last place every single season until they won it all". That is not true. They came last ever since they started in 1962 to 1967. In 1968, the year earlier, The New York Mets came second to last where as The Houston Astros came last. In 1966 the Cubs were in last.
At the stadium, when Griff is showing J and K the future game, right after he says the line "A miracle is what seems impossible...", in the shot from the back his hands are on their backs but on the shot from the front he is holding their hands by the elbows
In the first Men in Black, when K is deleting J's history; He deletes his birthday which was in 1975. The third film is set in 1969 and when K meets a young J, he is about 7 or 8. This would mean he was born no later than 1962, not 1975.
When the 1969 cops have J pulled over, before pressing the button on the neuralizer, he is not wearing his glasses, but in the next shot, he has them on, despite the fact that he didn't have a free hand to put them on.
When J is charging Boris and keeping track of the spikes that the alien shoots at him so he can dodge them on the second try, Boris first shoots and hits J in the left shoulder. Then the second shot hits J in the right as J says "right" and the third shot hits his left side. Then when he goes back in time a few seconds, the only thing to change is J knows the sequence of which Boris will shoot the spikes. Only it is different. J dodges the first one and says "right" as it passes his right side. Followed by two lefts, and then a forth one on the right. Yet previously, it was left first, then right, and then left again only three. It goes from left right left, to right left left right.
As J pops his head up on the tall building, there are windows immediately behind on his right and left and both are closed. The camera pulls up and back to show the scale of the building, then cuts back down to J. Now suddenly the window on his right side is open, and the lamp in the room is on. The window also changes from closed to open a few times in this scene.
When they are leaving the first crime scene (the crashed UFO) in their Ford Taurus they are shown talking with headrests in the vehicle. They arrive at the headquarters for Zed's eulogy. After the eulogy they are back in the Ford Taurus and the headrests are gone.
When the woman is about to be sucked by the void and fiercely grabs Boris' wrist, the wide and close-up angles show her using her left arm, however in several close-ups it's the right arm shown, as noted by position of her thumb, style of the bracelet (from grey rubber to black with diamonds), and a ring appearing/ disappearing.
When J steals the blue car keys, a nerdy looking guy with an orange and white striped shirt and glasses is walking towards the hotel. After J drives zooming through New York, the same guy is seen crossing the street walking the opposite way.
When Jay encounters Boris at the Cape, he travels back in time a few seconds. Rather than inserting another copy of himself into the time line, as they both did in the earlier time jumps, he relives the event, effectively giving himself a "do over".
The bowl K is holding while telling J he is going to be suspended for 2 weeks, then 4 weeks, changes positions. K sets it down upright, then J says he quits and its upside down, then it's back upright.
In the scene where J is being questioned by K, O walks up to to K, who picks up a cup of coffee and starts drinking it. The handle is directly in front of K on the opposite end of the cup in the first shot, but in the next shot, the handle is suddenly on the other side.
When Boris kills Ronan the Fabulist, the spike he shot at his head is located to be just an inch or two above his eyebrows. When J finds the body a few moments later, the spike is suddenly much further up his head than it was a few moments ago. The spike has also shifted an inch to the left.
When the Lunar-Max guards take Boris' girlfriend to visit his cell, one of the guards opens the door. Just as the shot finishes, the cell door can be seen open enough for two people to stand side by side. From the other side, there's only enough room for one person.
This movie starts in 2012 as shown on Zed's memorial, then travels back to 1969, 43 years earlier. But J tells the young K "25 years from now you're going to recruit me, and 14 years after that, the guy you didn't let me kill today..." That's only 39 years.
After K has placed the ArcNet on the Apollo rocket, he goes down a zip line and meets up with the Colonel on the beach. The shot from the zip line shows the colonel to be standing on the sand. Next shot, he's suddenly standing on the arrow signs between each zip line.
As J is being put in the "big ass neuralyzer", they first have him in front of it strapped in a metal bracket. As they begin turning him upside down, the white suit guy on the right reaches over and begins opening the hatch on the neuralyzer. You see him turn the handle and hear the creak and see it slowly crack open for a moment before the shot cuts. Then two shots later as the white suit on the left is about to put the bite guard in J's mouth, the hatch is suddenly closed and the guy on the right is reaching over to open it again.
Boris' girlfriend is first shown to have a tattoo with "Boris" over her back. A few minutes later, after Boris says "I'm a bit of a romantic", the Lunar-Max guards walks over to the cake in Boris' girlfriend's hands and the tattoo on her back is shorter.
When Boris' pet emerges from the cake, it kills the two guards. The Lunar-Max guard that had his hand stuffed in the cake has a spike put in his head and lands on the floor with his head resting against the cell wall. After the pet removes Boris' shackles, Boris goes to leave the cell and the guard with the cake on his hand is now lying on the floor almost entirely turned over.
As soon as Boris blasts the door down, there are guards on the grounds and guards behind some of the cells in the background. After Boris blasts the the steel wall, the guards on the grounds are sucked into the vacuum of space, but the guards hiding in the cells in the background have vanished completely. They certainly weren't sucked into the vacuum of space because they were protected by both the cell bars and the ceiling above them.
When the huge alien fish throws J through the window of Wu's, J knocks over several rows of frogs hanging in the window as this happens. As he finishes being thrown out of the window, only one row of frogs is left. A few minutes later as K suspends J, K goes to exit Wu's and now there are suddenly two rows.
At the diner, J says to the waitress K has apple pie. K is then given some apple pie. In one shot, the waitress is in the middle of giving K the plate with pie and the plate has not reached the table yet. But in the immediate shot afterwards, the pie has already reached the table.
When J puts a tray in the fish's mouth, it swaps from perfect to wrinkled between the first two shots in a time-frame. For the rest of the scene, there's no continuity between the shape it has in the wide angles and in the close-ups.
At the Apollo rocket launch platform, J calls Boris the Animal twice, who lifts J up and launches him away. J glances at K, who's got both arms stretched out trying to save himself. A shot later, in the close-up, only his right arm is stretched out.
When J drags Warhol backstage, the people they pass-by have no continuity between the front and back shots. Note the tall transvestite with bulky hair they bump into first, who, a shot later, appears several meters ahead.
When J exits the Flatiron building in 1960 a woman walks right behind him, then the shot cuts to his POV of a group of hippies, then back to the previous shot of J and the woman obviously continues her walk. She should've been several meters ahead already.
When J chases Boris in 1960s New York he exits The Factory and runs on the sidewalk past a black car and a lamppost. A frame later, the car is gone and he's running on the pavement, on the space left, to allow him to step on the green car.
After K is falling with J from the rooftop, big chunks of concrete start to fall, yet disappear in some shots. When they land, the ground is clean, yet in one of the close-ups of K a chunk magically reappears next to his head.
In the Headquarters in the altered time line, when J is crying out that he and K spent 14 years of stakeouts, cowboy music, etc. A woman in the back swaps from standing by a screen to walking 20 feet to the right, between shots.
When past and future Boris meet, past Boris turns towards future Boris completely and has his full body facing future Boris as he is walking toward him. But as future Boris is still walking towards past Boris and saying the line about spending the next 40 years in prison, past Boris suddenly has his body turned away from future Boris, and so future Boris has to step around in front of past Boris.
When K returns to the diner to leave the tip, he places down the money with his left hand and his finger is still on it as the shot ends. As it cuts to the next shot he is suddenly pulling his right hand away from the money.
When Griffin shows J and K the vision of the baseball game, J walks back and then walks back over to Griffin. Griffin then places his arm around J and his hand ends up around the top of his arm. In the next shot, Griffin's hand is suddenly on J's shoulder.
After busting out of the cake and killing the two Lunar Max guards, Boris' hand creature goes to free him. It first blasts spikes at the shackles on his legs and busts them, then begins climbing up to work on Boris' arm piece. In the shot where his leg shackles come off, you see the spike the creature shoots at them stuck in the metal and hanging off to the side. But in the shot where his arm piece falls to the floor, these spikes have vanished from his leg shackles.
When Jeff sets the box with the time device in it on the counter, he begins to open it with one hand on the side of the box, and the other hand on the front of the box. It cuts to a close up and suddenly his hands are both on the sides of the box.
When the racist cops are frisking J, one pulls out J's gun and questions him about it. In the reverse angles, the cop is holding the gun over J's shoulder with almost all the handle in his hand. In the shots showing J's face, the cop is holding the handle so that some of it is sticking down, and it is in front of J's shoulder.
When K tells J he's suspended after asking about Boris, they get into a brief confrontation about it. As K is storming away to take the car, leaving J back at Wu's without a ride, J's suit is still dirty, wet, and nasty from his fight with the alien fish. Moments later, J is seen going to MiB headquarters and now his suit is clean and in perfect order.
On the Apollo docking bay, just as J says "You're gonna lose", Boris has J pinned up against the scaffolding. Then as Boris says "Let's agree to disagree", J is suddenly not pinned against the scaffolding, leaning forward. J also goes from looking ahead to looking down.
As the hand creature busts the shackles off Boris' legs in Lunar Max, you can see the bottoms of his pants over his metal prison boots. There are only a few folds and wrinkles over his left foot, and the pants over right foot are hardly wrinkled at all, or affected as the creature climbs up his right leg. But only a couple of seconds later, we see another shot of Boris' feet as the creature breaks off the metal sleeve of his arm, and suddenly his pants legs are very wrinkled. Boris was standing perfectly still the entire time. Boris' legs are also suddenly closer together.
When J is digging through files to try and find out what happened between Boris and K, O comes in and talks to him for a moment. As she is leaving, shots of J shows he is leaning back in his seat. But when O is shown, the glass wall she is by shows his reflection, leaning forward and slouching.
As Griffin is telling J that K has to go to the Apollo launch, the shot from his perspective shows J holding his nose from where K punched him, his hand being over his nose. The shot cuts to show Griffin's face and suddenly J is wiping the underside of his nose.
As J flies backwards after the fish creature sneezes, he breaks through the plate glass window, and has the bottles in his hands. After the cut, he's just breaking the glass, and the bottles are missing from his hands.
When Jeff is talking to J on the Flatiron, he is looking at J except for a brief shot where strangely he is suddenly facing left without having turned his head. Then a frame later, from another shot, he is back facing J.
When Boris asks the guards in Lunar Max to cut up the cake for him and his girlfriend, she turns towards the guards holding the cake. Her head is leaning slightly forward and tilted to the right. The camera cuts back some and suddenly her head is tilted left and back.
As Boris says "I see you've brought me a treat, darling" to his girlfriend in Lunar Max, she turns her head from the guards and looks at the cake. It cuts to a closer view of Boris' face, and instantly she is looking at him instead of the cake.
As J is telling K the truth about Boris killing him at the Moon Launch, one shot from behind K shows his head is down. The next shot, he is suddenly looking straight forward as he punches J in the face.
When K slaps Wu with the Spikey Bulba the first time, you see Wu's head turn to the right as he's hit from the over the shoulder view. But when it cuts to show Wu's face, his head is suddenly being thrown back rather than turning right.
As J is saying no jet packs, he has both arms out with his hands turned palm down. It cuts to a different angle saying there's a reason they don't have those in the future, and you can see his left hand. It is suddenly gesturing towards the machines but palm up.
After being pulled over by the racist cops, J insults them and they pull him out to frisk him. As they have him bent over the car, one of them pulls out his gun and says "what's this, a concealed weapon". In the shot from behind J turns his head to the left to look at the gun. It cuts to a view of J's face as he says "Hey, it's his grandmother's suit." J is instantly looking straight forward.
After the incident at Wu's restaurant, J walks up to a crowd of people and says "Can I have everyone's attention please?" As he does, he holds up his neutralizer. Just before the cut, you see him raising his other hand and points at the device. It cuts to show the crowd, then back to J. Suddenly he is repeating this exact same motion, the footage repeated as he points to the neutralizer.
When J and K are talking to Agent W backstage, as Agent W says "You're out of your mind...", he is looking straight forward at K, head remaining still. Next shot, he is looking at K with his head is suddenly shifted to the left.
After J shows Jeffrey Price the news report of the Boglodites, Jeffrey asks J "What's the plan?" and J is then shown raising his shoulders and placing his gun back into his back pocket. In the next shot, you can see J begin to do raise his shoulders in the same fashion as he did in the previous shot a second time.
When they arrive at the ball park, K gives J his stuff back. The close up of the time device in J's right hand shows his thumb is closed in close to his hand. But the shot cuts to show both him and K, and suddenly his thumb is stretched out. K also puts his arms down twice during this part.
At the diner, K asks J if he has a girl in the future. In that shot, J is looking down at his food. It cuts to a different angle and J is instantly looking straight forward as he is turning his head to K to say "I got you."
At the diner, K says the "pie don't work unless you let it." J then looks at him and begins waving his fork at his own pie, but the shot cuts to a different angle and J is instantly looking down at his pie as he begins waving his fork.
When Griffin is telling J that his buddy might give him antacids for his gastric distress, there is a small group of people behind him. One of them is wearing a picnic cloth style dress with red and white squares as the pattern. She walks away to the left of the screen, but then it cuts to a close up of Griffin as he says "But that depends" and she is suddenly right behind him.
When J is in his lying fest at the 60's MiB headquarters, he starts calling two guys that walk past him "K." The first one walking by has a clipboard he is working on. He walks totally past J, and then another guy with nothing in his hands begins walking by and is almost passed J. Then the camera cuts to a close up of J, and the second guy passing him suddenly has stuff in his hand he is working on.
As K is questioning J in the past at the MiB headquarters, there is a green alien behind J talking on the phone. In the close up of J as he's telling K to turn the power down on his tazer, and he can't feel his tongue, the MiB agent behind J is seen taking the phone from the alien and hanging it up. It cuts to K saying "How do you know my name?" then back to J in a shot further away. The green alien is seen handing the phone to the MiB agent again to be hung up.
After the timeline is altered, J returns to MiB headquarters where he is met by Agent Double A in the elevator. After a brief monologue by Double A, J turns to him and says "Give me 5 feet, or I am gonna pluck you in your throat." He holds up his hand like he is going to flick Double A. In one shot, his wrist is bent forward, but in the next shot, it's bent back.
Jeffrey begins giving J a quick crash course on how to use the Time Jump device on top of the building. Just before he says "When you're moving fast enough" he pats J on the back, receiving an angry look from J. Jeff then puts his arms down as J begins slowly moving forward. The camera then cuts to a closer shot as he begins that line, and suddenly Jeff's arm is back on J's back, and J's arms are in a different position.
Trying to crush the metal tray that J wedged in its mouth, the large alien fish breaks a tooth on the tray. J then picks up a couple of bottles of mustard and squirts its nostrils full. During that shot, the shape of the broken tooth has changed slightly, and the remaining piece is larger.
Just before K says the line "I used to play a game with my dad..." at Wu's restaurant, he is looking straight forward. But as he begins saying that line, preceeding a sigh, the camera cuts to a different angle and suddenly he is looking to his right.
As J and O are talking about temporal rifts, after J states Boris was on Lunar-Max, O says "If Boris could figure out how to time jump, he could seriously change the course of history." In this shot, her left hand is raised and her fourth finger is shown to be placed on her thumb. Next shot, her finger and thumb are no longer touching and her finger is now pointing to the right.
After Z's memorial has ended, J and K are driving. As J says "Because I was too tight", he is looking at K, doing a mime for tight with his right hand as the line ends. Next shot, he's looking straight forward, not doing the mime anymore.
In the car after Z's memorial, K asks J, "You lose something over there, Hondo?" As he finishes this line, J is looking at K, sitting up. In the next shot, J is looking at K with his back resting against the car seat.
Just as K begins his eulogy of Z, a voice is heard saying "And now a few words from Agent K." In this shot, J is shown with O on his right, and an alien with a cranium for a head on J's left. Between J and O and behind them is a balding agent. Between J and the cranium headed alien is a female agent. But in the reverse angle of J, O and the cranium headed alien, the balding agent is suddenly behind J, not behind both J and O, and the balding agent is suddenly much closer to the female agent.
After Boris has blasted a hole in the steel wall of Lunar-Max, Boris grabs onto his girlfriend's arm who is getting sucked into the vacuum of space. The first shot shows his hand wrapped around her wrist. A few shots after, his hand is further up her arm.
During the scene where Agent J and K are driving around Midtown Manhattan, the wide shot shows them driving past the red TKTS staircase in the middle of Times Square. Then there is a shot of J inside the car a few moments later, and they pass by the red TKTS staircase again.
After K remembers to leave a tip, the meteorite that was intended to land on Earth ends up hitting a satellite. The shot returns to Griffin, where he is shown to be looking uncomfortable and turns his head back round. Then as he says "That was a close one" in the following shot, he is suddenly looking calm and smiling.
When Boris is questioning Roman The Fabulist about where the Arcanan is, Roman has a cigarette in the corner of his mouth. When Boris takes off Roman's hat, the cigarette has moved to the center of his mouth.
When Griffin places his arm back around J's shoulder after J steps back, J is shown to be looking at the baseball field. Next shot just as J says "So this is how you see things", J's head is suddenly slightly shifted to the left.
After the time jump has finished, J is shown lying two feet above the ground. The first shot shows J to be looking very shocked with his eyes wide open. Then in a close-up, his eyes are suddenly almost half closed looking exhausted, and his head is shifted to the side. Then in the next shot, he's suddenly back to having his eyes wide open, looking shocked.
In the "Oh, man. This coffee tastes like dirt." scene, Agent K says:
"How you know my name?" then picks up a cup of coffee with his right hand, passes it to his left hand and raises it to his mouth. The camera changes and K is seen holding the coffee cup in his right hand.
As O is helping K into the jet pack harness, he asks her if that is right. She says "Unfortunately it is." In that shot, she is looking up at him right into his eyes. It cuts to a side angle and she is suddenly looking at his mouth and chin.
After J arrives in 1969 and leaves the Chrysler Building (42nd St and Lexington Ave), he looks across the street to a building labeled as the Roosevelt Hotel. The Roosevelt is at 45th and Madison Ave. In 1969, the Hotel Commodore was across Lexington from the Chrysler Building (the site now occupied by the Grand Hyatt).
When Boris escapes from the Lunar Max he passes an incorrectly complete Apollo lunar module (see factual errors), and as the shot zooms out from the moon it is clear that the location of the Lunar Module is nowhere near any Apollo landing site.
In the scene where Agent J has jumped from the Chrysler Building, the Manhattan street configuration and building arrangements are not accurate. East 43rd Street does not continue west past Lexington Avenue, as depicted in his fall. And the entrance to the Roosevelt Hotel is actually located at Madison and East 45th, not on Lexington Avenue across from the Chrysler Building's west facade.
When on the moon in the beginning, the Apollo lunar module is shown with the upper ascension module. This module was launched off of the moon to return the astronauts to the orbiting module to return to Earth.
J jumps from the roof of the Chrysler Building, which is 925 feet high. He falls for more than 30 seconds before activating the time jump device. Given the height of the building and the acceleration of gravity (32ft/s2), it should take less than 8 seconds to reach the ground (9 seconds if air resistance is taken into account).
The ARCNET device is shown activating shortly after the second stage separates, and the launch abort tower is jettisoned, which happens before Saturn V reaches even the low orbit. While at that altitude the sky would indeed appear black, as shown, the Earth behind the rocket is obviously too far away - it would appear like that from about half way to the Moon.
Saturn/Apollo stacks were taken to the launch pad with the launch tower preceding the rocket stack. They are shown with the Saturn/Apollo stack north of the launch tower instead of the other way around.
The uppermost swing arm of the launch tower is missing the "clean room" that allows access to the Apollo capsule before launch. It was normally moved away from the capsule several minutes before launch.
When J goes to the electronic store to get the time jump piece from Jeffrey Price, all of the TVs in the store are showing "Wheel of Fortune", which in NYC is shown on ABC TV channel 7. But when the show is interrupted for the emergency story about the invasion, the TVs show NBC TV Breaking News, which is channel 4 in NYC.
When J arrives on top of the bird on the Chrysler Building in 1969, he looks around at the view. The North Tower of the World Trade Center (One WTC) should be in view. The construction of the North Tower began in the summer of 1968. In 1969, even though the very top was still under construction. The first tenant moved in. Even though One WTC wasn't officially finished until 1972, in July 1969, there should be a clear view of at least 3/4 of that tower.
In 1969 while Boris is riding his motorcycle on the boardwalk in Coney Island, he rides in front of Nathan's Famous. In 1969 the only Nathan's Famous was on Surf Avenue. It wasn't until approximately 35 years later, in the mid 2000s, that Nathan's opened a smaller satellite store physically on the boardwalk.
When J is driving to Coney Island and is stopped by the two police officers,the view of Coney Island in the background is wrong. You see the Wonder Wheel ferris wheel and to the right you see the Cyclone roller coaster. The only way you could see the Cyclone to the right of the ferris wheel would be if you were on the boardwalk, on the beach, or in the Atlantic Ocean. (The tall cylindrical ride between the coaster and wheel is verification that the roller coaster shown is the Cyclone.) In addition, in 1969 there were two other roller coasters - one of of which would've been seen in that view - the Tornado which would be to the right of the ferris wheel which means the proper view should be two roller coasters with the ferris wheel between them.
The motorcycle ridden by Boris the Animal has an low-profile rear wheel and tire which were not made in 1969. However, given that the motorcycle burns with a blue-green flame after it crashes, it is probably reasonable to assume it is at least partly of extraterrestrial manufacture.
Lunar-Max prison is obviously part of MiB, them creating it for the purpose of holding Boris the Animal, and other criminals of worth as well. A high tech prison built on the moon with cutting edge technology and armed guards out the boot. Boris trashes the place, sounding all kinds of alarms and busting out, even blowing a sizable hole in the side of one of the complexes. He then jacks a ship off the moon's surface and crashes it back down to Earth. MiB doesn't know about it until almost a full day later when they realise the ship they found was from the moon, and Boris had escaped. It makes no sense that it took them that long to find out the information. A maximum prison, especially one to contain aliens on the moon, would be in contact with MiB. And any alarm that goes off there, especially for a break out of a high danger prisoner such as Boris the Animal, would have sent an alert to MiB headquarters right off if there was any logic to their system at all. There is only about a 1.5 second delay for a message traveling at light speed to reach Earth from the moon due to its distance. So within seconds of Boris busting out, MiB should have already been mobilizing to track where he would be going and intercept. There's no way, that logically, Boris could have escaped, made it back to Earth, and been there for nigh a day without MiB knowing about it and having their agents already tracking him down.
When (future) Agent J and (future) Boris are fighting on top of the large red docking station for the spaceship, Agent J gets shot deliberately by Boris and jumps off the edge of the dock. Then he uses his time travel device to go back in time a few seconds earlier to be able to dodge the shots. There are a few mistakes in this part. 1) There should be another Agent J and Boris there too, as they have gone back in time to that moment again. However in the movie there are only two of them. 2) The injuries sustained by Agent J (the bone spikes in his abdomen) should have remained there when he went back in time. If it were true that you healed once you went back in time into the condition you were in at that moment, then Boris should have grown an arm back when he went back in time. 3) Due to the time loop, Agent J remembers how to dodge the shots, while Boris doesn't remember anything and is surprised by the outcome.
At the ball park stadium, K, J, and Griffin are high up in the bleachers watching a future window of the Mets game. Boris suddenly drives by on a motorcycle up in the stands and grabs Griffin, then plows through the railing on the side of the stadium and falls down below, crushing K's car. He then speeds off instantly out of the parking lot with Griffin. Then suddenly, somehow, J and K are running out into the parking lot close to their car quickly enough to be watching Boris speed away from the parking lot on the road. There is absolutely no way K and J could have made it out of the stadium and out into the parking lot in just a couple of seconds like that.
The US Army & US Air Force call their jails or prisons "stockades" or "guardhouses". The US Navy & US Marine Corps use a "brig". The Colonel directed his US Army Military Police to take Agents J & K as well as Griff to "the brig".
The goof items below may give away important plot points.
In the climax of the film, J lets Boris shoot him three times so that he can memorize the pattern, go back in time, and dodge the shots. When Boris shoots the first time, there are three shots: one to J's left shoulder, one to his right, and a third to his left side. J even says the locations to himself, illustrating his desire to remember them. However, when J goes back in time and dodges the shots, Boris shoots a completely different pattern, including an extra shot: first he shoots to J's right, then two shots to his left, and a fourth back at J's right. Somehow J still calls and avoids all four shots.
After Agent J returned to the present on top of the Chrysler Building near to the end of the movie, the next shot seems to show the view of the Empire State Building from his point of view. In fact it's a view from the GE Building at Rockefeller Plaza.
In the first Men in Black, when K is deleting J's history, he deletes his birthday which was in 1969 (according to his birth certificate). In this one, James is shown as being about 4 or 5 in 1969. This would mean he was born no later than 1965, not 1969.
In the altered timelime where K is killed in 1969, Agent J's career should have been erased from existence because K recruited James Edwards from the NYPD to the MIB in Men in Black, but in the new timeline K would have been dead for 28 years before that happened. So who recruited James in the new timeline?
J used the time device to go back while fighting Boris at the end on the Apollo launch platform. When he went back in time there should have been two agent Js. Either that or when Boris went back in time he should have switched places with his younger self, and then there would be only one Boris.
In the altered timeline where K is killed in 1969, Jeffrey Price shouldn't remember, that he helped Boris to move back in time, because Boris wouldn't have been imprisoned and wouldn't escape from prison to kill K in the past.