Revealing mistake: When Marty begins to slump down due to fading from existence look at the guy playing the piano behind Marty, he's not even pressing the keys on the piano just putting his palms on them repeatedly.
Visible crew/equipment: When Marty asks if the time machine is nuclear, a boom microphone is visible in the right windows of Doc's van. (00:26:28)
Continuity mistake: George's hair fixes itself when he tells Marty about Darth Vader coming down to visit him. It's initially messier.
Continuity mistake: Before Marty kicks the speaker while playing Johnny B Goode, there is a case of Pepsi below it which disappears between shots.
Continuity mistake: When Doc and Marty are looking for his dad at school, you can see a girl with a blue sweater going downstairs twice. (00:56:49)
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. (01:02:35)
Continuity mistake: After George knocks Biff behind Marty there is a couple running to George, but in the open view they disappear.
Continuity mistake: When George is checking the time at the prom there is a girl in grey behind him that changes to one in pink. (01:18:56)
Continuity mistake: After Marty gets to the square in 1955 his hair changes after he grabs the newspaper.
Continuity mistake: When Marty arrives at 1955-Lyon Estates he removes his hood and his fringe is brushed from right to left. When the angle changes it has swapped sides.
Continuity mistake: Right before Doc presses the remote control to send Einstein to the future, his left index and thumb fingers are on the remote. In the close-up it's just his thumb on it. In further close-ups it swaps to the index and thumb.
Continuity mistake: Before Doc sends Einstein to the future and says "If my calculations are correct...", Marty raises his left arm. When the angle changes it's lowered.
Continuity mistake: While Marty is talking with Jennifer in the square he is holding a tape case in his left hand which disappears in the next shots.
Continuity mistake: While Doc is explaining to Marty how the machine works, he has a device on his index finger on his right hand that moves in the next shots.
Continuity mistake: While Marty is at Lou's Cafe, Biff and his gang enter. When Biff starts bullying George, note George's haircut with shaved sides, back (above his neck), and sideburns. In the following shots, George's haircut with its shaved areas change length. This happens again, when George is with Marty and then tries to ask Lorraine to the dance. (00:39:00)
Continuity mistake: Throughout most of the film, the licence plate on Doc's car reads 8N 39742, but after the DeLorean travels back to 1985, it changes to 7F 42857. (01:41:31)
Revealing mistake: As the DeLorean's tyres start igniting as it is about to travel back in time, the flames are not coming from the tyres, but from some ignitors attached to the car. (01:40:36)
Continuity mistake: When Marty approaches the couple, the couple goes down a step twice. (01:07:03)
Continuity mistake: When Marty skates off after knocking over the couple, the car behind him is red and cream, but in the next shot, it turns completely red. A yellow car also appears in the second shot, when it was not present in the first. (01:07:10)
Chosen answer: I think that is *exactly* what he is thinking. He realizes that by standing up to Biff, George may have irrevocably changed his personal future, and therefore affected Marty's future as well. This is exactly the sort of thing Doc was so eager to prevent by refusing to hear any information about the future.
Phil C.