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)
Continuity mistake: After Doc Brown sends Einstein one minute into the future, the rest of the scene until he returns is played out in real time. There are no scene cuts, and any camera angle changes are accompanies by continuous audio which negates any possibility that time has been stretched or compressed. However, it takes Einstein 1 minute 21 seconds to return.
Continuity mistake: Whilst George McFly is pegging out the laundry, Marty is explaining his plan as to how he can make Lorraine fall in love with him. At the start of the scene, both of Marty's breast pocket flaps are untucked. After putting the bag down, one tucks itself in, then they return to normal when Marty says "let's go over the plan again". (01:09:55)
Continuity mistake: When Biff and gang are chasing Marty on the skateboard, they eventually crash into the rear of a manure-hauling dump truck. When the car swerves left in an attempt to miss it, it will obviously pull somewhat to the left. In the shot just before impact, you can see that just the rear half of the car should impact the truck, but in the next shot the car rests perfectly centered behind the dumps open load. (01:07:25)
Factual error: In the skateboard chase scene, after the crash, a crowd gathers. In this crowd there is a kid dressed in a Cub Scout uniform. He has a red/white town strip patch on his arm. In 1955 the Cub Scout town strip patches were blue with gold lettering.