Continuity mistake: When Marty stops the Delorean in front of the Lyon Estates sign after escaping the farm, notice the sun - it's overcast and kind of foggy. When he looks at the sign from another angle, it has become more sunny, and later in the day. When the couple with the car passes, it has returned to the same as before.
Continuity mistake: When Marty confronts George as "Darth Vader", after George asks "who are you?" Marty plays the music again, and George presses his hands to his ears. In the shot from behind, his hands are cupped around his ears, in a very different position. Then when Marty says "silence earthling", in the shot from the front his hand is away from his ear entirely.
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. After the truck makes a right turn, notice how the two kids he initially stopped to get a skateboard from at the beginning of the scene suddenly appear standing at the street corner between shots, holding their wooden crates. (01:06:25)
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.