Continuity mistake: When Marty gets locked in Biff's garage, we see that he can't push through the two garage doors because there's a lock on the other side. Yet, when Biff comes out to go to the Prom dance, he opens them in literally no time at all with no resistance. We don't even hear him unlock them.
Continuity mistake: When Biff is trying to run down Marty on the hoverboard, as he comes out of the tunnel there is a shot of the manure truck driving down the road. Cut camera angle to Biff missing Marty and hitting the truck, which is now at a dead stop, however there was not adequate time to do this and appears that the truck was driving then instantly stopped.
Continuity mistake: When Marvin, the band member, goes to call Chuck Berry about Marty's "new sound", the telephone he uses has a black neoprene coiled handset cord. In the first BTTF, the phone had a straight, uncoiled brown cloth handset cord (seen when he says, "Well then listen to this." and holds the handset out toward the stage). This isn't because the cord was stretched out, as neoprene cords can't stretch so much that they look uncoiled.
Continuity mistake: At the start, the DeLorean hits the left dustbin and comes to a halt. At the other side of the street, there is only one car parking near to a house. From another angle there's a different red car parking on the other side of the street, and the tree that stood between both houses has gone. (00:01:15)
Continuity mistake: When the rain stops after Marty and Doc first get out of the DeLorean in 2015, Doc looks up at the rapidly clearing sky. Directly above their heads the sun is shining brightly. However, if you look at the tops of the buildings you can see sunlight hitting them from the sides. I suppose we will have another sun by 2015? (00:06:42)
Continuity mistake: Right at the start of the movie where Doc Brown pulls up on the drive of Marty's house, we see a panning shot as Marty and Jennifer walk to the DeLorean - there are no vehicles parked on that side of the street. A moment later as Marty waves his hand in front of the Doc's glasses, there's a green VW bus parked almost outside the house. Then as the Doc's looking through the rubbish bin, the VW's moved further down the street. Then as the DeLorean backs off the drive, there's a yellow VW bus there instead. (00:01:20 - 00:02:05)