Factual error: The movie is set in 1882, however there is a scene where he meets Doc Brown with his DeLorean. Back to the Future Part III took place in 1885.
Continuity mistake: The sheriff wears his badge over his left side, which is traditional. As he is approaching on horse in the final scene of the movie it is still on his left side. Then for a few seconds in one shot his badge is on the right. (01:23:10)