Continuity mistake: After the dance, when Marty arrives at the clock tower in Doc's car (across the street from the DeLorean), he parks precisely midway between the two stores. As the clock tolls, Marty jumps into the DeLorean, and, in the overhead shot as Marty drives off, Doc's car is directly in front of the store with the blue awning. (01:31:20 - 01:36:00)
Continuity mistake: After Einstein comes back Doc Brown is demonstrating to Marty how to set the time machine. He simply pushes the buttons on a key pad. To set it for July 4, 1776 he punches 3 buttons. To set it for December 25, 0000 he punches 6 buttons. To set it for November 5, 1955 he punches 12 buttons. Later, when Marty is resetting the time machine to go back 10 minutes early he punches 7 buttons (all not including the ENTER button on the keypad). (00:23:50)
Continuity mistake: In 1955, when George walks into his house, Marty thinks of Mystery Science Theatre and looks at the vanishing photograph, and at the dance, after George punches Biff and rescues Lorraine, again Marty looks at the vanishing photo. In these two close-ups the thumb holding the photo looks nothing like Marty's thumb/nail in other close-ups, such as when he powers up the amp at Doc Brown's at the start. (00:03:15 - 01:23:45)
Continuity mistake: When Marty tells George how to flirt with Lorraine, they both enter the diner and Marty sits on the back of the counter but disappears between shots, only to reappear later on. Also, the extras around him change, although they're all dressed in similarly colored clothes. Check a man in a plaid jacket next to the blonde girl in pink, who disappears when Marty trips Biff. This continuity havoc was due to the combination of Eric Stoltz scenes and new Michael J. Fox reshoots.
Continuity mistake: When Marty is up on stage "disappearing" and yells "George..." (wanting for George to resume the dance with Lorraine and ultimately kiss her), this exact shot of Marty shows him slumping over and appearing very weak, almost on his knees. A split second later showing that same scene (right when George finally walks back to Lorraine) only from the "crowd view", Marty is still standing upright, not slumped, maintaining his composure.
Continuity mistake: In the scene at the beginning of the film where Marty cranks up his giant amplifier, the resulting explosion blows Marty into a shelf which tips over, spilling all of its contents on top of him. In the next shot, despite the shelf having been emptied in the previous shot, papers and file folders continue to fall on Marty.
Continuity mistake: After Goldie Wilson arrives at the manure truck scene, we can see onlookers approaching at the street corner in front of Texaco - one of which is the kid who Marty borrowed a skateboard from. But once the shot changes, that same kid is instantly standing on the sidewalk near Marty holding a crate instead. (01:07:35)