Factual error: At the end of the movie, when the new time machine built into a steam locomotive begins flying and departing, the train signals are still running and the barrier crossings are still down. The train signals should have stopped once the flying time machine locomotive was off the tracks.
Suggested correction: Train signals generally stop once the end of the train is a good distance away from the road where the signals sit, by sensors. In the film, the train is too close to the road and by lifting up in the air, the sensor to stop the signals were never reached by the train.
Continuity mistake: When Marty is about to race against Needles, he holds the wheel with both hands. An instant cut later, his hands are gone.
Revealing mistake: When Clara's dress rips off and is about to fall off the train, Doc saves her. One can notice it's not Christopher Lloyd but his stunt double. (01:41:17)