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.
Revealing mistake: At the end, when the train destroys the time machine, right at the moment when it hits you can see a small explosion, which was used to trigger the destruction of the time machine.
Continuity mistake: When the train is coming and is about to run over the DeLorean, the shadow of the train on the wall shows that it is only the locomotive. When the camera changes view, it is a train with freight carriages.
Factual error: At the end of the train scene just before Marty travels to 1985, the train busts through a road block warning that there's only 1/4 mile of track left before the ravine. Keep in mind that the train is travelling at approximately 70-80 mph by this time. At 70 mph (and not even accelerating) it would only take the train 13 seconds to reach the ravine. The actual time in the movie is at least a minute.
Deliberate mistake: When Marty is being chased by the Indians, a wide shot with the DeLorean at the bottom of the screen coming towards us and the Indians following reveals the entire background for a mile or two. However, there are no cavalry visible anywhere despite the fact that they pass over the cave in the following shot only five seconds after the last Indian does.
Continuity mistake: When Clara first sees the train and starts after it on horseback, it is on her right side. She is at the top of a hill and starts down after the train. In the next shot shown from the front of the train you see the horse appear so the train is on Clara's left.
Other mistake: When Marty returns to 1985 from 1885 the time machine is destroyed by a train. What is strange is that not only does the train not stop (which is mandatory in the event of an accident) but there is also no reaction from people nearby, such as those in the vehicles waiting to cross the track at the level crossing. Later, when Marty returns to the site with Jennifer, there is still no sign of police officers or other officials.
Factual error: When the red Presto-log is burning, rivets begin to blow out of the locomotive, supposedly from the pressure. The rivets in the boiler, which would be subjected to pressure, are not visible on the outside of a locomotive. The rivets which are seen to blow out in the movie are in the smokebox, an area which is subjected to heat and smoke, but no steam pressure.
Continuity mistake: When the DeLorean is being pulled by horses, the clouds in the sky change in the next shot.