Continuity mistake: When Marty is about to race against needles, the camera zooms in towards his car. Notice a big rectangular black object reflected on the car. From opposite angles it disappears and there's just green fields. The black object was most surely a structure to hide the camera equipment.
Character mistake: At the ravine, upon learning that the bridge doesn't exist yet, Marty states to Doc "We can't wait a year and a half for this to be built". If you carefully look at the sign, it says the bridge is opening Summer 1886. That's under a year away, not a year and a half from Sept. 1885.
Continuity mistake: In the end scene where Doc's train comes back to 1985, Marty and Jennifer are literally blown away by the re-emergence of the train. While they are flying in mid-air, the front of the train is passing them by and gets just about to the cab (where the ELB is). However in the next cut, Marty and Jennifer are on the ground watching as the train just starts passing them again, and the train comes to rest at a point before the previous "blown away" cut scene.