Continuity mistake: In 1955, when Doctor Brown is watching the video of himself, he sees himself saying that the Libyans are coming. You can hear a significant pause between "They found me" and "I don't know how but they found me." But in the beginning of the film he says the entire phrase without any pauses. (00:28:45 - 01:08:10)
Continuity mistake: In the cafeteria, when Mr. Strickland is glaring at Marty and Biff, the table Marty was sitting at with George is behind him. When Biff leaves there is a close-up of the table and both the lunch tray and Marty's jacket have changed positions significantly from the previous shots (George had already left). (01:00:30)
Continuity mistake: As Marty drives the DeLorean towards the clock tower, if you look carefully you can see that he drives past the 'Bluebird Motel' billboard at least 3 times (which is where he started from) and drives past that small building with the slanted grey roof in the square about 4 times.
Continuity mistake: When George goes into the cafe to tell Lorraine he is her density/destiny, the people sitting at the bar keep changing with different shots. Best example is just after George refers to his "density" - in the background there's a brunette in a blue jumper at the bar. A blonde woman and a short-haired guy then sit on her left, but then disappear in the shot of Marty sitting at the bar - on the brunette's left there's now another brunette in a pink jumper with a different guy. The brunette's got shorter hair too. In the very next shot the blonde's back with no sign of Marty. (01:02:10)
Continuity mistake: While Doc is waiting for Marty to get back from the dance, he looks at the watch on his left hand, his pocket watch, and the watch on his right hand. When he looks at the watch on his right hand, he is wearing it on the inside of his wrist. Then, as he is running around the car, he has no watch on his right wrist at all. Moments later, as he is pointing down the street, it is on the outside of his right wrist. When they are checking the alarm clock, he holds it in front of the alarm clock to check the time, and the watch is still on the outside of his right wrist. (01:31:15 - 01:32:30)
Continuity mistake: In the scene after Marty returns to 1985 he jumps out of the DeLorean to verify he's back and then jumps back in the car to go save Doc at the mall. In the shot where he's putting the car in gear, you can read part of the yellow "Last Time Departed" display on the time circuits as "1985, 1:20AM", and in the shot where he's trying to start the car, you can read "Oct". It should read "November 12, 1955, 10:04PM" since that was the time he just left. On top of all that, the display appears to relate to when Einstein traveled a minute into the future (you can see when Doc shows Marty the time circuits after he lets Einstein out that the "Last Time Departed" is "October 26, 1985, 1:20AM"), not when Marty traveled back to 1955 (October 26, 1985, 1:35AM). You could argue that the "Last Time Departed" display is not working properly, but Doc uses Marty's last time departed (October 26, 1985, 1:35AM) to set Marty's destination time when he's returning to 1985. (01:42:40)
Continuity mistake: When Biff chases Marty out of the cafe in 1955 and Marty 'makes' the skateboard, there is an odd shot of a tree. When Biff's car drives through the grass, the big tree in the shot is shaking violently, yet all the trees are completely still during the chase before and after this shot. During this entire scene, differences regarding varying degrees of windy then calm, wet vs dry pavement and variations in shadows cast are numerous. (01:06:30)
Continuity mistake: When Marty arrives in 1955, he puts the DeLorean behind the sign, and walks into Hill Valley. When Marty and the 1955 Doc come back later, the DeLorean is facing the other way round to what it was at the beginning (you can tell because at the start Marty pushes the BACK of the DeLorean AWAY from the Lyon's Estates billboard, but when they come later, the FRONT is facing TOWARDS the billboard). (00:35:05 - 00:51:15)