Deliberate mistake: During the train sequence at the end of the film in 1885, it is blatantly obvious that the train is not going the speed that the DeLorean's speedometer is showing. In some shots, the train looks as though it is going little more than 20mph. (01:38:55)
Deliberate mistake: In the duel with Marty, when Tannen gets fancy spinning his gun, when he places it in the holster the grip is facing forward. They then use effects to turn the gun so the grip is facing back. (01:26:44)
Suggested correction: No, the gun is spinning on his finger and goes into the holster with the grip facing towards the back, which is completely consistent with the spin of the gun.
Deliberate mistake: When Marty drives towards the screen to go back to 1885, he passes by the same 5 speakers over and over again. It's obvious that the road was very short and they repeated the shots from many different angles to add-up for tension.
