Factual error: Though extremely modest on today's standards, the dress worn by Clara to the hoedown shows far too much cleavage for the time. No schoolteacher would ever wear a dress like that in the 1880s.
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. (00:18:10 - 00:20:00)
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.
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. (01:43:03)
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. (01:43:00)
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. (01:40:31)
Continuity 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. (00:19:15 - 00:20:20)
Revealing mistake: When Marty and Shamus are sharing a meal at the dinner table, Shamus passes Marty the plate of rabbit. As Shamus hand moves away to let go of the plate, to the bottom right hand corner of the plate, a purple patch appears briefly where the two M. J. Fox actors interact, an error with the Vistaglide camera tech used back then. Easier to spot on Blu Ray Version, better than DVD. (00:24:10)
Factual error: Standard gauge for railroad tracks in 1885 was 4ft 8 1/2 inches. The distance between the center of the wheels on a Delorean was 5ft 3 inches. The car would not fit on to the tracks, and we can see the wheels aren't recessed or otherwise altered.
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. (01:34:09)
Continuity mistake: When the DeLorean is being pulled by horses, the clouds in the sky change in the next shot. (00:38:50)