Continuity mistake: In the first BTTF movie, when Lorraine and Marty are sitting in the car, Lorraine takes off her coat and then asks Marty why he's so nervous. In this movie, when Marty is crouching down to get past the car, Lorraine looks at 1955 Marty and asks him why he's so nervous without taking off her coat.
Deliberate mistake: When Old Biff and Young Biff are sitting in Biff's car, the car's rear-view mirror vanishes during all shots of Old and Young Biffs together. Presumably this made the split-screen effect easier to do.
Plot hole: If Old Biff changed his past and went back to 2015, he goes back to HIS future, not the bad future, but Doc later tells Marty that if he were to go to the future to stop Biff from taking the almanac, he'd go to the bad future, so Old Biff technically shouldn't have been able to return to "his" future at all.
Continuity mistake: When Biff punches Marty in the stomach, he falls to the ground between Biff's henchman. The camera angle changes to a wide shot and Marty is still on the floor but he's about 3 feet in front of the henchman now.
Revealing mistake: When Biff cocks his revolver in the alternate 1985, you notice that the chambers rotate in the wrong direction. This is either a flipped shot or a mistake caused by the prop gun.
Revealing mistake: As Doc and Marty go to the soon-to-be Lyon Estates in 1955, the DeLorean hovers over the camera. Look at the roof. You can see 3-4 wires attached to the time machine.
Continuity mistake: At the clock tower scene at the end of the movie, you can see the DeLorean drive past a line of shops that are about 25 yards from the clock tower itself. However, in the next shot of the DeLorean, you can see that it has only gone about 50 yards from the Bluebird Motel (where it started from). In addition to this, even if there were some identical shops further up the road that Marty went past (which there more than likely aren't), you can't see any on the next shot. These shots are chronologically incorrect.
Continuity mistake: In the beginning of the movie, when they reenact the last scene from the first movie, Marty asks Doc how he's going to turn out in the future. Doc pauses briefly, then says "No no no, you and Jennifer turn out fine." He doesn't pause in the first movie.
Plot hole: After Biff steals the DeLorean and travels back to 1955 with the Sports Almanac the movie states that he creates an alternate timeline. Doc Brown does a good job of illustrating this on a chalkboard. So if, as Doc Brown states, Biff created an alternate timeline, then when he travels back to 2015 it would be the alternate 2015. Even if the original timeline stays intact with Doc and Marty in it, they'd be trapped there because Biff took the Delorean and returned it to the new timeline, not the one they're in.
Suggested correction: When Doc explains to Marty the events that changed the timeline from 1955 onwards, several hours have passed since they returned from the (original) 2015. Old Biff likely returned to the original 2015 not long after after giving young Biff the almanac, so it is entirely plausible that not enough time had passed for the alternate version of 2015 to take ahold. When Doc tells Marty if they were to go back to the future they would be going to an alternate future, enough time had passed for the future to turn into the alternate future.
Continuity mistake: At the end of Back To The Future, when it shows Marty and Jennifer talking to Doc, Marty is tanned, but at the start of this movie when the scene is repeated, he is pale.
Continuity mistake: When Doc Brown lifts off in the Delorean just after Marty gets the Almanac from Biff, Doc does a full right turn on the steering wheel, but the next shot shows the Delorean turning left in the air.
Revealing mistake: When old Biff and young Biff are discussing the Sports Almanac in young Biff's car in the garage, young Biff tosses the Almanac into the air, landing in the back seat next to Marty. When it's thrown in the air his hand and the Almanac become transparent.
Continuity mistake: At the end of the preview for BTTF3, Marty and the Doc are standing in a position for their photo to be taken. The photo is taken, but on the photo their hands are in different positions to what they were when the photo was being taken.
Revealing mistake: When Griff and his gang are flying through the air and about to crash into the courthouse after the hover board chase, look at the girl on the left. Her legs hit one of the building's pillars, and her body rotates sideways, but she continues moving forward - obviously suspended by wires.
Revealing mistake: During the hoverboard chase in 2015 between Griff and his gang and Marty, you can plainly see the wires holding the gang up on their hoverboards in the wide shots as well as on the Jeep Wrangler before it lands in front of Marty.
Continuity mistake: In 'Part 1,' after Doc crashes into the trash can, Marty waves his hand in front of Doc's torso. In 'Part 2,' he waves his hand in front of Doc's glasses.
Revealing mistake: When Marty is burning the almanac, during the lightening strike, the shadow of the post holding the hover-board off the ground is visible. - watch the hoverboard when the scene is illuminated by lightning strikes. The post holding up the hoverboard is also clearly visible when they pan around Marty as he is holding the burned rope from the Delorean.
Continuity mistake: In the Cafe 80's sequence we see little Elijah Wood and his friend investigating the Wild Gunman game. One of them asks "How do you play this Thing?" while Marty is several feet away, but Marty answers immediately while standing right next to it. So he has managed to walk about 15 feet or so in a fraction of a second.
Continuity mistake: In the tunnel chase where Biff is catching up with Marty, the speed of his car changes from going fast and gaining speed to driving at normal speed a couple of times in different shots. The distance between Marty and the car also keeps changing with this.
Continuity mistake: When the DeLorean first lands in the alley in 2015, there is a shot of the back of the car as it lands. The large vents that extend out of Doc's modifications to the car are the wrong size. In most shots, they extend over the car's tail lights, however in this shot they stop above the lights. According to commentary this is a fiberglass scale model of the DeLorean used to film flying scenes, since it is lighter than the actual vehicle, so apparently the model was not quite identical to the real DeLorean.
Suggested correction: The effects of the past being altered may not have happened immediately. It is possible that it took time for the timelines to adjust to the changes of events, meaning enough time would have passed to change 1985 when they return, but not enough time could have passed to change 2015. By the time Doc says if they went back to 2015 they would be going to an alternate future, some time has passed, so the effects of the past being altered and taking ahold in 2015 and altering it are more likely to have occurred by then.
Casual Person
Here is what you say: "perhaps it took time for the time lines to adjust." What kind of time would timelines take? Time is time, it doesn't take time to change the timeline. That doesn't make any sense. Some people claim it was the DeLorean itself that came back to its own original timeline and only then reset itself in the new one, but then the new timelines being erased later on wouldn't have happened either. So its a genuine plot hole.
lionhead
It's established in the first film that it takes time for the changes to take effect. Marty and his siblings slowly disappear from the photo, rather than instantly. Although the scene in BTTF2 was deleted, it was filmed showing Biff dying and slowly fading away after his return to his present.
Yet they were restored instantly without any outside influence at the end of the movie. There are a lot of things wrong with this movie and the first one. Old Biff disappearing should mean that Marty and Doc should slowely disappear as well, even the DeLorean. But they didn't, that doesn't make any sense. The point is there is a plot hole, somewhere. To know where all you can do is look at it logically and then you automatically come up with Old Biff going back to the future but not the alternate future. If he did there wouldn't have been a movie, but that's the plot hole.
lionhead
The timeline didn't change until he made his first bet which was some years I think after receiving it. He immediately travelled forward after giving the act, meaning he will still jump forward to the original future.
The timelines would instantly change, and Old Biff couldn't possibly have returned to "normal" 2015. It's just a poorly-thought-out time travel plot hole (or a deliberate error to expedite the storyline).
Charles Austin Miller
Suggested correction: In context, Doc was saying that they couldn't return to 2015 to stop Biff from stealing the time machine, because Biff didn't steal the time machine in the alternate 2015, he only stole it in the original 2015. Marty and Doc didn't stay long enough in 2015 after Biff returned, and that's why they didn't see any differences. Also, though they were unaware of it, Biff was dead in the alternate 2015, so the disasters he caused might have reverted back after his death.