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 arrives in 1955, he 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?
Continuity mistake: When Marty drives out of the Peabody barn after arriving in 1955, it's night, or certainly pre-dawn - the sky is very dark from every angle when he's fired at while driving away. Next shot he drives past the "Peabody ranch" sign onto the main road and it's significantly brighter, with the sun rising over the horizon. Then when he notices the Lyon Estates sign shortly afterwards it's broad daylight - judging from the length of the shadows the sun's very high in the sky. Lyon Estates isn't that far from Twin/Lone Pine(s) mall.
Other mistake: When young George and Marty are in the backyard talking about what will happen at the dance, young George hangs up clothes to let them dry, but if you look closely the clothes are actually already dry.
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.
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.