Continuity mistake: In Biff's apartment in alternate 1985 while Biff and Lorraine are arguing he knocks her to the ground and both her shoes come off. After Biff punches Marty in the stomach it then switches again to show Lorraine's reaction. As it does this we see her on the floor but her shoes are back on her feet. She could have had enough time to put them back on possibly but it seems unlikely that she would have done so as she is laying in the same position as when she was knocked down.
Revealing mistake: When Marty, in the 1955 dance, looks at his father with his binoculars, you can see that the angle of the binoculars are really misplaced. Marty is looking at him at his far front, but the binoculars' image comes more from the floor. In fact, what the binoculars show is from the first film.
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: When Marty gets the sports almanac in the tunnel, he flies on the wall with his left foot in the hover-board's strap. When he flies over the car and lands on the hover-board, his right foot is in the strap of the board. After that it keeps switching legs and in or out of the strap. (01:33:00)
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.
Continuity mistake: In the scene after Marty is leaving the school hall after his performance, Lorraine and George bump into him backstage and Lorraine says, 'Marty that was very interesting m... music' with a stutter. However in the first film when she says the same line in the same scene she says it without a stutter. It is meant to be exactly the same line and scene from the previous movie.
Other mistake: When Doc, Marty and Jennifer have arrived in 2015 Doc tells them that the time of the day is 4:29pm. However the destination time is still shown on the time circuits' display from their time travel to the future - the two times should match, but the destination time has the bottom AM/PM light illuminated, while the current time has the top one lit. They didn't arrive or leave at 4:29am, so something's wrong somewhere.
Other mistake: In the scene where Biff confronts Marty outside the swinging doors while Marty is watching himself talk to his 1955 Mom and Dad, you can see that Crispin Glover (George McFly) has been replaced with Jeffrey Weissman. There are other scenes where you can tell it isn't him, but this is the most prominent one. Glover wasn't in the 2nd movie due to him and the producers not agreeing to a movie contract. All the scenes you see him clearly were taken from the first film. (i.e. where Marty is looking at him through the binoculars at the dance). (01:27:59)