Continuity mistake: When Marty goes back from 1955 to 1885 and meets the Indians, note that none of the Indians shoots any arrows nor do any arrow hit the car. You can see that when he drives the car back into the cave. But when he gets back to the cave after the Cavalry ride, a long arrow sticks out on the side of the car.
Trivia: Looking at the three films at a whole, we can note that no fewer than FOUR DeLoreans were simultaneously existing in 1955: (1) the one in which Marty comes in the first movie; (2) the one in which the old Biff comes in the second movie to give the Sports Almanac to his younger self; (3) the one in which Marty and Doc come in the second movie to rescue the Sports Almanac; and (4) the one which Doc hid in a mine in 1885 to be found by Marty in the third movie.
Trivia: When filming the scene where Marty is being hanged from the clock tower, Michael J Fox agreed to really hang from the rope. Whilst filming, Fox held the rope away from his throat with his hand. At one time he wasn't holding the rope and was really being strangled. The film crew didn't realise, they just thought it was really good acting, until he passed out.
Question: At the end of the movie, Jennifer asks Doc about the note she got from the future that became erased when Marty did not participate in the race with Needles. Doc's answer to her question is that her future had not been written yet, and he goes on to say that no-one's future has been, but if that is so, then how come in the previous movies he could travel into the future with Marty to see Marty's future?