When Marty and Doc talk about going back to 1955, whenever the camera is focused on Marty, you can see what looks like some sort of mechanical device or someone using the equipment outside of the window. This can be seen between 01:01:56 and 01:01:57 and also 01:02:03 and 01:02:06
As Marty is crawling across the electrics position above the stage at the enchantment under sea dance in 1955 you can see a few lighting fixtures hanging there in the background. You can see a Altman 360q Axial Ellipsoidal Reflector Spotlight which wasn't introduced until around 1971.
As Doc and Marty are about to travel back to 1955, Marty says, "What about Jennifer? What about Einstein? We can't just leave them here." When he says this, the shadow of the boom operator and boom microphone can briefly be seen above him and on his t-shirt.
In the alternate 1985, Marty's former neighborhood is now a high-minority neighborhood with frequent murders, as evidenced by the chalk-outlines in the street. Despite this danger, the daughter in the family that lives in his old house sleeps with the window open.
Doc doesn't interfere with the police officers picking up Jennifer, saying that the officer wouldn't believe that he and Marty were time travelers. However, these same officers accepted without question that Jennifer was her older self, despite her youthful appearance, because of her thumbprint. Marty's thumbprint also would not have changed, so he could easily prove to the officers that he is his older self, Jennifer's husband.
At the beginning of the movie, Doc assures Marty, "you and Jennifer turn out fine". Marty and Jennifer were far from fine in 2015: Marty lost everything and married Jennifer in Vegas, and even Biff comments to Marty (thinking that he is Marty Jr.) that Marty Sr. "flushed his life down the toilet".
In all the scenes of Young Biff and Old Biff riding in the car together, the car has no rear view mirror on the windshield. When Young Biff first comes back out and gets into the car again ("I'm going to the dance, ma"), it still has no rear view mirror, yet after he backs out onto the street and it then cuts back to the shot looking in toward the windshield, a mirror is present.
When old Biff steals the time machine to change the past, he returns the Delorean back to 2015 so Doc and Marty would suspect nothing. He should instead have arrived in the alternate version of 2015 just like Marty and Doc went to the alternate 1985. No explanation is given as to why he can return to the unaltered time-line while Doc and Marty can only get to alternate versions of the time-line.
When Biff and Marty watch Fistful of Dollars on TV in 1985A, Joe (Clint Eastwood) is first shown wearing his hat, but when Ramon (Gian Maria Volontè) shoots at him, the hat is missing. This is due to editing - the shot of Joe wearing his hat is from an earlier scene in the film.
At the dance, the original 1955 Marty (the one playing the guitar) doesn't say "Try and" (like he did in part I) before saying "keep up" to the band.
Also Marvin Barry goes to the audience's left to make the phone call to Barry (not behind the blue tinsel curtain either), while in the original, he either was off to the right or off to the left and behind the tinsel curtain (based on the placement of the curtain on the left that is seen in part I).
As young Biff is chasing Marty through the tunnel after Marty gets the almanac back, Marty pushes off with his right foot with his left foot on the back of the board (riding goofy). Later, as an upper body shot of him is shown, Marty is facing the other direction, with his left foot on the front of the board (riding regular).
The license plate on Marty's truck (in the garage) is different in the re-shoot of the scene at the beginning of the movie. In the original the plate reads "2EYP916" (or similar, it's hard to read exactly but it does end with 916). The plate in BTTF2 reads "2BAK860".
In Back to the Future part 1 when Marty Mcfly was playing "Johnny B. Goode" and when Marvin Berry made the phone call to his cousin, the phone had a straight wire. But in the Back to the Future part 2 the phone had a curly wire.
When Strickland and Marty are talking to each other in the alternate 1985, there are cracks in the sills around the window and the front door. When the car full of armed "slackers" starts shooting at them, the cracks in the sills disappear.
When Biff is unconscious, Marty kneels next to him, unzips Biff's jacket, and is seen reaching in for the Almanac. In the next shot Biff's jacket is zipped again and Marty's knees are above Biff's chest.
When Marty and Doc are getting ready to go back to 1955 to get the sports almanac, Doc makes a point of turning the time circuits on. However, they were already on, which is evidenced right before this when they are shown to be malfunctioning.
When Griff is taunting Marty in Café 80s, behind Marty outside the window, there are two men talking to each other (standing next to a red X). After Marty ducks to avoid being hit by Griff's bat, the men have disappeared,
When the DeLorean lands in the alley in 2015 with the tires folding up, it comes to a final rest with the front tires sticking out slightly past the front fenders. In the next shot from the front of the car, the tires are tucked up under the fenders as they are throughout the rest of the first and second films when shown driving on the ground.
When Biff confronts his old self in his car in the street after chasing the girls and shouting "I'm going to marry you one day", Biff is wearing Levi 501 jeans with the red tab on the right rear pocket. Old Biff then drives young Biff to his house and old Biff stuffs the Almanac into young Biff's right rear jeans pocket - which no longer has the red Levi tab.
When Marty is sneaking into Strickland's office, the US and California flags are next to each other, away from the stack of books on the desk. In the next shot, when Marty reaches to move the US flag, the California flag has already been moved next to the books.
Just as Doc drives up behind Biff (just before they enter the tunnel), the Doc turns the wheel of the Delorean off to the left and also turns his head in that direction but the exterior shot shows the car going right.
Doc has a watch on both wrists. The one on his left hand alternates from dial-in to dial-out throughout the film. Most noticeable right at the beginning when they are arriving in 2015. It is inside his wrist as they arrive but outside when he get out of the Delorean.
When Marty walks out of the alley (where the DeLorean first lands in 2015) we see a dark blue car with a white stripe taking off. In the next shot of the same runway, there's a light blue car taking off.
When the police put 1985 Jennifer in her 2015 house it was dark outside when they opened the door. However, when the camera was facing Jennifer on the couch, you can see that the shoot was filmed in the day by looking at the window behind Jennifer. Then after Lorraine pulls up the scenery screen in the next scene it's dark again.
In the end of Back to the Future, when Marty and Jennifer are interrupted by Doc, Marty is not wearing a wristwatch. But when the scene was re-shot for the opening of Back to the Future Part II, Marty is wearing a wristwatch.
While Marty is being chased through the tunnel by young Biff, Marty's stance on the hoverboard is left foot forward or regular. A split second later the stance is right foot forward or goofy pushing mongo (Front foot pushing). A second later the stance is regular again then it switches back to goofy pushing mongo. Then in a quick shot it's regular again. And at the beginning of the movie his stance is regular.
In the ally way in 2015 when Marty is putting on the jacket Jeniffer's arm is laying on something blue. But when Doc Brown presses the size adjustment button on Marty's jacket, Jeniffer's arm is now resting on something beige.
During the tunnel chase, where Biff tries to run Marty down, his foot is shown not in the strap on the hoverboard. But when Marty is rescued by Doc his foot would have to in the strap in order not to leave it behind.
In the opening scene the background vehicles change in several ways. The VW Bus changes position and color first green then tan. It also goes from next door to two houses down. The Chevrolet Suburban across the street changes from the original mid '60's era to a early '70's model. Its position also changes slightly.
After the DeLorean first lands in the alley in 2015 and the camera pans around the car, Marty opens the passenger door and the door mirror is folded back. However it was not folded back when they departed from in front of his house in 1985, nor is it folded back later in the movie.
Right after Doc, Marty and Lorraine have arrived in 2015 and Doc takes off his mask, some residue from the mask is stuck on both sides of Doc's nose. In the next cut, as Doc starts running, the residue has inexplicably disappeared.
When Marty retrieved the sports almanac from the garbage can in Strickland's office, it was the almanac cover wrapped around a girlie magazine. However later when Marty grabbed the almanac from the unconscious Biff, the almanac was intact with the original cover.
When Marty does the "switcheroo" in the hotel stairwell to avoid rich Biff's thugs, a crewmember's shadow is visible at the spot Marty jumps to. This can be seen right before the camera pans upwards to reveal Marty a few flights up running towards the roof.
When the DeLorean is following behind Biff's car and Marty is climbing along the side of the DeLorean towards Biff, a wheel used to roll the "hovering" DeLorean along the ground is visible underneath the front right tire.
There is no way fifty years worth of horse races, MLB games, NBA games, NHL games, NFL games, (as well as every other game mentioned) would fit into a book the thickness of the almanac used in the film.
When Marty, Jennifer and the Doc first arrive in the future it's raining. Despite traveling at 88 mph or above, the rain on the passenger windows of the DeLorean runs vertically down. Air velocity at that speed would push rain back faster than gravity would pull it down.
When they travel back in time from 2015 to 1985 and the passenger airplane flies by, there would not be readily-visible brightly-glowing engine-flames unless the plane had afterburners. Only military jets have them; civilian jets have all of their combustion-chambers "deeper" (farther back inside) within the engines.
While in Alternate 1985, Doc Brown shows Marty the Newspaper which features Doc getting committed to a mental asylum, and one of the other articles on that same paper reads "Nixon Seeks Fifth Term in Office". The alternate time line was created when Old Biff traveled back from 2015 to 1955 to give Young Biff the sports almanac and from the events which stemmed from it. This means that, for all intents and purposes, that prior to November 12th 1955, there was no alternate time line, and all the historical events leading up to that date remained the same. This being said, there was no way Nixon could've sought a fifth presidential term in either time line, as the Twenty-Second Amendment (which limits any US President to seek no more than two full terms in office) was passed by Congress in 1947 and ratified by the states in 1951. Unless Biff's historical-meddling had managed to screw up the time line so much so that it would affect the US Government of all things (which is very unlikely), then even in Alternate 1955 onward, the two-term presidential limit would've still been in place, and even if Nixon had not resigned his presidency in the Alternate time line and served his two full terms in office, his presidency would have ended in 1977 and he would not have been able to seek reelection for a third term much less a fifth.
While the events the film outlines in 2015 cannot be considered errors for obvious reasons of fiction and fantasy, the notion that Chicago and a new team in "Miami" could have ever met in the World Series IS a mistake for a simple reason: even in 1989 when the then Florida, now Miami Marlins were in the planning stages, Major League Baseball had made it clear that its planned next round of expansion (to take place in the early 1990's, which ended up actually being 1993) would permanently put both new teams in the National League. The reason for this is that the American League at the time had two more teams than the NL and the league wanted the leagues to have the same number of teams. While it would take a long time and many other moves to fully realign the two leagues (including the change from four to six divisions with a wild card game, an expansion AL team in Tampa Bay, Milwaukee moving from the AL to the NL and Houston doing the opposite), neither the Marlins nor Cubs were ever considered for an NL-AL move. That makes the idea behind this scene a mistake in any context.
The 50-year Almanac has only a few dozen pages, and so the sports stats for 1955 would be listed just a few pages in from the front cover, yet Old Biff opens the book to a random spot that's clearly much nearer the middle of the book.
When Marty arrives in the alternate 1985 and sneaks into the house he thinks is his own, a Dirty Dancing (1987) poster can be seen on the girl's bedroom wall. If history was changed, Dirty Dancing could have been released in an earlier year, but Biff only changed the history of Hill Valley, not anywhere else. So if only Hill Valley is different, everywhere else would've been the same. The secondary headline in the "Emmet Brown Committed" newspaper which read "Nixon to seek Fifth Term" wouldn't have worked either as Biff didn't get himself into politics, and even if he did he wouldn't be able to make changes in the Constitution.
When arriving in 1955 at the Lyon Estates sign, the flux bands on the flying DeLorean are lit up blue on the flying model and remain on until we see the car landing behind the sign. They are only supposed to light up when hitting 88 miles per hour. They are never lit up after entering and exiting the wormhole.
When old Biff returns to 2015 after giving 1955 Biff the Almanac, he should have returned to an alternate future where Biff was rich not the same 2015 he left earlier. This is explained to Marty by Doc later when Marty questions whether they can go to 2015 again to stop old Biff from getting the almanac.
After Doc and Marty bring the unconscious Jennifer back to her house and leave her on the porch of her home, the next shot shows the twin Lyon Estates "concrete" walls at the entrance of Marty's street. No city anywhere would allow private builders to construct a "sign" like those on city property, (anything from the beginning of the sidewalk to the street) but especially NOT on the actual street which would be a driving hazard.
In the tunnel scene, as Biff is preparing to chase Marty, the car's front tag is dated 1951. California-registered cars had 1951-dated license plates in 1955; a small metal "55" tab was placed over the "51" stamped into the plate to keep the registration current.
Assuming time travel was possible as described in the movie, you couldn't travel into the future and see your older self. As you skipped the intervening period by time traveling, your older self would not exist in that time line. This would be possible as long as you returned from the trip. If they could not have returned, I.E. If Marty died in the future, then it would not have been possible.
Marty's Japanese boss in 2015 is called "Fujitsu-san". Fujitsu is not a real Japanese last name, but the contraction of "Fuji Tsushinki" (Fuji Telecommunications), "Fuji" being likewise the union of the first syllables of "Furukawa" and "Siemens" ("Si" is pronounced "Ji" in Japanese"). It is very unlikely that a Japanese person bears that name, which is actually a trademark. The gag is that trademarks and commercialism have gotten out of hand in the "future."
The audience assumes that Biff's gun is a standard six-shooter like in all the old Westerns, but in fact, Biff's revolver is a Smith & Wesson Model 60, which has a five-round cylinder. Biff clumsily blasts away at Marty five times while chasing him through the mansion, so there is no way he could have gotten off another shot when confronting Marty on the roof ("Jump off the roof, or you'll die of lead poisoning!") without reloading. But because Biff's gang was chasing Marty to eventually the fire exit stairs, Biff himself could've gotten some bullets to reload his gun.
Some viewers assume that when the police take Jennifer home and they tell her "to be careful in the future". This implies that they either know that Jennifer is from the past or a time traveler and that they wouldn't be "in the future" at least from the police officers point of view, but rather in the present. They don't have such knowledge, implied or otherwise, they're obviously referring to the future of 2015 Jennifer, although it might also be a play on words by the writers.
When Doc and Marty arrive in the alternate 1985. (unbeknownst to them) they leave Jennifer on a porch with the idea that she would just wake up at her house. Later on its revealed that they are in a very dangerous neighborhood where nobody in their right mind would be in such a vulnerable position. She was left there for hours and her whereabouts are never addressed and she is never even seen again.
When Marty sees George deck Biff, we see the Marty from Back to the Future running out to the parking lot. When he glances at the photo and splits, the couple he runs in to are completely different to the actors in the first movie and they don't say anything to each other, whereas they should have been seen to say 'Who is that guy?' 'That's George McFly.' 'THAT'S George McFly?' as they did in the first movie before Marty bumps in to them. Furthermore, when Lorraine is picked up off the floor by George, we see his hair is shaved very close at the back and sides, but in the next shot the new actor playing George who leads Lorraine away doesn't have closely shaved hair.
When you see the DeLorean landing in Hill Dale (2015) you can see that the shot obviously changes from the shot of the model to the 'real' car. The cooling vents on the back of the model car are clearly darker and smaller than on the actual Delorean, they don't cover the tail lights at all.
The miniature Deloreans used in effects shots have no key locks on their doors, making it easy to determine whether a model or the actual vehicle is being used in a scene. This is especially true in shots where the car is touching down, and split screens are used to mask the transition from model to full-size vehicle.
When Marty confronts Biff about the Sports Almanac; Biff pulls a revolver and points it at Marty. There are no bullets in the gun; otherwise, the tips of the bullets would be visible in the cylinder. There are blanks in the gun which are shorter and not visible.
When Marty is talking to the alternate 1985 Biff, Biff pulls a lock box out of the wall safe and opens it. He pulls out the Almanac to show Marty and Marty reaches out to take it before Biff pulls it away. Marty was clearly trying to take the book away from Biff, but there is no real reason for him to do so because taking the book back then would not alter the timeline back to the original 1985.
When the DeLorean is hovering behind Biff's car before entering the tunnel, as Marty is getting out of the car onto the hover board, a brief view of the time circuits shows yellow displays on top, green in the middle, and red on the bottom. The red display (destination time) should be on top, and the yellow display (last time departed) should be on the bottom. This same shot also reveals that the driver of the DeLorean is not Doc, but a stuntman who is clearly trying to obscure his face from the camera.
When Doc holds up the news paper showing the article about Marty Jr. getting arrested, underneath it is an article about how cholesterol could be the cure to cancer. However, both articles talk about Marty Jr. stating "Protesting that he was "put up to the whole thing" by a local gang, Martian McFly Junior (17) was arrested today...". Then, the article reappears in the newspaper about Griff. In addition, at the bottom of the paper, it says "Coming: McFly insists that the gang..." on both copies.
When Biff starts in on Marty with "You think that stupid disguise is gonna get past me?" he challenges Marty to a fight and Marty says, "No, Thanks," and turns to exit the shot. The edge of the window in the background is the split. When Marty turns, the brim of his hat just barely crosses the line, causing it to disappear for a few frames.
The DeLorean that lands in the alley in 2015 has smaller cooling vents, thrusters for hover mode. They do not overlap the tail lights of the car like they are shown to everyplace else in the movies. It also appears to be smaller in every dimension.
When, in 2015, Marty presses the drying mode on his jacket, the jacket tells him "your jacket is now dry" when it is clearly still wet. He's not wearing an actual dry jacket until the next scene when he goes to give the girl her hoverboard back.
When Doc and Marty return to 1955 and land behind the Lyon Estates billboard, Doc opens the trunk which is covered in fresh ice, but it doesn't appear to hurt his hand as it did in Back to the Future after sending Einstein one minute in to the future.
After the hover board scene when Griff and his gang are being pulled out of the courthouse and Griff says "I've been framed" you can see the wires holding the camera that takes the picture, if this was supposed to be hovering then it wouldn't need wires to support it.
In the alternate 1985, Biff corners Marty on the roof of the casino. Throughout the whole scene there are curved lines around the corners of old Biffs mouth where the latex prosthetic skin appears to begin separating from the actors cheeks as he is delivering his lines. It's especially evident when he says the line "Besides,they couldn't match up the bullet that killed your old man."
The goof items below may give away important plot points.
When 1985 Doc comes across the Delorean under the canvas in 1955, his hair is clearly styled as 1955 Doc's. It is only in the next scene (in which the two Docs chat) is his hair back to its normal "wild" self.
At the end of the movie, when Doc and Marty are chasing Biff to retrieve the almanac, and Marty hops out of the DeLorean and on to the hover-board, he straps his left foot into the strap and he is wearing red Nike's. Later when he gets off the hover-board, his right foot is in the strap and his Nikes appear to be blue.
Near the end of the film when Doc instructs Marty to burn the Almanac he 'drops' the hover-board. It can then be clearly seen sitting on a mechanical post - you can see it and it's shadow every time the lightning flashes.
When the DeLorean is hovering and is struck by lightning, it isn't moving 88mph. However, the letter Doc sent from the past explained that "the lightning bolt that hit the DeLorean caused a gigawatt overload which scrambled the time circuits, activated the flux capacitor, and sent me back to 1885," so it's not a plot hole.
When old Biff and young Biff are discussing the Almanac in young Biff's car in the garage, young Biff tosses the Almanac into the air, landing in old Biff's lap. It is clear that the Almanac, while in the air, is animated not only due to the animation quality, but also that it had no reflection in the hood of the car.
At the end of the film the original Marty and the Delorean travel from 1955 back to 1985. After the Delorean has leaped back to the future it left twin fire trails on the pavement behind it. As Doc is dancing between the fire trails, it's quite obvious that the filmmakers left some type of flammable padding on the roadway wherever fire is burning, probably to protect the road itself.
When Old Biff hands Young Biff the Almanac, the book passes through the film split (the vertical bar that divides the windshield) perfectly because it was on a motorized rig. But the stand-in for Old Biff didn't hold his arm at the right height, so Old Biff's arm disappears into the bar that runs down the middle of the window while the book floats across to Young Biff.
Just before 1985 Doc meets 1955 Doc, while 1985 Doc is talking to Marty on the walkie-talkie, the shadow at the base of the lamppost changes as the camera moves around, but it is not 1955 Doc's shadow - it is an artifact from the job of splicing the two bits of film together.