Continuity mistake: When Marty is about to go to 1885, before Doc shoots his gun, you can see the coils on the face of the DeLorean is brown, later when he is driving toward the screen, the coils are clear silver again.
Continuity mistake: As Doc reacts to the icy DeLorean, the door Doc was about to pull open barely has any ice on it, but when Doc opens the door with his foot, more ice is on it, then melts after Einstein runs back into Doc's truck. (00:24:00)
Continuity mistake: When Goldy (or Golby?) says, "Mayooorr", George is facing Marty. Then when Goldy starts saying, "Now that's a good idea," George is facing Goldy, without any motion of turning. (00:40:35)