Continuity mistake: After the train crashes against the "Tracks end" sign, the editing is all wrong: Marty is inside the car covering his head with the hover board. Half a second later he has magically moved outside the car, dangling and holding the hover board. Then we see Clara upside down, and back to Marty back inside, removing the hover board from his head after the crash. then he dangles outside with the hover board. So the first shot of him dangling shouldn't have been there.
Continuity mistake: When Buford chases Marty, the position of his 3 goons is an absolute mess and changes from shot to shot with no continuity whatsoever: Sometimes they're behind Buford; or two riders on the right and one on the left; or last but not least: all three riding past Marty until a shot later one of them suddenly appears way behind the group.
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.