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 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 A Fistful of Dollars on TV in 1985A, Joe (Clint Eastwood) is first shown wearing his hat, but when Ramon (Gian Maria Volonté) 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).
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 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.
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 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.
In Back to the Future part 1 when Marty Mcfly was playing "Jonny Be Good" 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.
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.
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.
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.
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 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
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.
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.
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.
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.
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.
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."
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 travelling, your older self would not exist in that timeline.
Old Biff steals the time machine in 2015, goes back to 1955 to change the past and returns to the original 2015. When Marty and Doc go back to 1985, Doc explains that history had been changed and that going back to 2015 would be the alternate future. By this logic, the old Biff should not have been able to return to the original 2015 as he did.
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 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 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 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 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 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 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.
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.
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 Marty finally fishes the sports almanac out of the Mr. Strickland's trashcan, he is horrified to find out that it is only the cover of the sports almanac; Biff has used the sports almanac's cover to hide the girlie magazine he was looking at. Yet throughout the rest of the movie, the cover of the almanac is shown once again attached to it even though Marty left the cover in Mr. Strickland's trashcan. How did Biff get the ripped-off cover back?
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 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.
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 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.
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.