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.
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.
Continuity mistake: When Marty gets hit by the car and wakes up in Lorraine's bedroom. She constantly calls him Calvin. Marty says "Calvin, why do you keep calling me Calvin"? When he says this he puts his arm on his lap. In the next shot behind him when Lorraine replies, his hand/arm is by his side.
Continuity mistake: When Marty lands on Peabody's farm and rams through the pine tree he then hits a scarecrow which flies over the top of his car. Then as they show it from the inside the scarecrow slams into the windshield - but how can it slam into his windshield if it is already over the car?
Revealing mistake: When Biff and his gang are chasing after Marty in their car around the Courthouse Square, in the shots that takes place in the Courthouse yard, you can see that it's Biff's stunt double that's driving.
Continuity mistake: Towards the very end of the film when George and Lorraine are unpacking George's new book, you will notice in the close-up of Lorraine's hands that they are actually someone else's for that shot. They are very aged and much larger than her real hands, which you can compare right away when the camera goes back to full view.
Continuity mistake: When Marty is on a skateboard being chased around the town square by Biff and his friends, he grabs the back end of a truck. He does with two hands at the same point, then uses one hand in the next shot, then two hands again.