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)
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)
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)
Continuity mistake: When Doc's about to send Marty back to 1885 from 1955, and Marty's dressed up...when Doc's walking back and forth loading up the car - look at the shadow from the building. You see it changes by several feet in a few seconds as the scene was obviously shot throughout the day. (00:16:35)
Revealing mistake: When Marty pours the wake-up juice through the funnel into Doc's mouth, in the close up the funnel is straight, but we can't see Doc. From a different angle where we do see the funnel stuck in his mouth, check the right side of the screen: The funnel is skewed (and seemingly it must have a tap) and the liquid is falling out in large amounts to avoid the actor from drinking it.