Revealing mistake: When old Biff turns to face Griff, his elbow passes through Marty's Pepsi bottle. (00:14:41)
Continuity mistake: Right at the start of the movie where Doc Brown pulls up on the drive of Marty's house, we see a panning shot as Marty and Jennifer walk to the DeLorean - there are no vehicles parked on that side of the street. A moment later as Marty waves his hand in front of the Doc's glasses, there's a green VW bus parked almost outside the house. Then as the Doc's looking through the rubbish bin, the VW's moved further down the street. Then as the DeLorean backs off the drive, there's a yellow VW bus there instead. (00:01:20 - 00:02:05)
Revealing mistake: When Doc flies the DeLorean up and the wheels get stuck to a banner string, the close-ups of Doc show a lit cockpit, but the shots from the outside show it's dark and one can't really see who's at the wheel. However, for a couple of seconds you get to see it's not Doc but a stunt double or a stiff dummy. (01:23:25)
Continuity mistake: When Doc turns the time circuits on as he is about to head over to the high school, the 'Destination Time' is under 'Last Time Departed', but in the next shot, it is back to being over it like normal. It should also be noted that the month is represented by a number in the first shot, but with letters in the second. Additionally, one of the LED's is burnt out in the first, but is back to being lit in the second. (01:23:30)
Revealing mistake: When Doc holds the newspaper with the 'Gang jailed' headline, the same paragraph is repeated several times. (00:24:03)
Continuity mistake: When Marty, Jennifer, and Doc head to the 2015 Hill Valley, part of the text on the dashboard is faded, but when they travel back to 1985, the text is completely intact. Additionally, in the second shot, the 'Last Time Departed' is mentioned as Nov. 12, 1955, despite it being Oct. 26, 1985. (00:38:22)
Continuity mistake: When Marty reads the paper with the news about his son's arrest, the way he holds the paper differs between shots. (00:09:44)
Continuity mistake: When Doc travels to 1885, Marty stands on the road holding a rope and says "He's gone." When the angle changes, the length of the rope sticking out is much shorter. (01:38:03)
Revealing mistake: As Doc drops Marty off behind Biff's car, the camera pans across the DeLorean, and we can see Christopher Lloyd has been replaced by a stunt driver. The stuntman can be seen trying to obscure his face. (01:30:26)
Factual error: When Marty enters the 1955 Hill Valley, one of the cars has a white licence plate with blue text and a sunset, which was not used until 1982. (01:04:54)
Continuity mistake: When Marty confronts Biff in the alternate 1985 in the hot tub, the girls change positions. The blonde was on his left and the brunette was on his right. When they see Marty and scream, they move forward but there is no way they can switch that fast. (00:55:40)
Continuity mistake: At the end of the movie, when Doc is running down the street after the DeLorean has gone back to 1985, the neon changes from red to yellow. It was red in both 1955 and 1985 in the first film. (01:41:34)
Answer: At the end of the first film, Doc says, "what the hell" in response to the letter Marty gave him. So this shows it is not that strong a conviction, especially in the face of definite knowledge about something bad happening. It is also a way for Doc to repay Marty.
MasterOfAll