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: At the start, when Marty and Jennifer kiss, Marty turns toward his parents standing at the door. The screen door has three lower sections, and the house numbers are black. When Doc says, "Where we're going we don't need roads," it then cuts to Biff rushing out the door. Now, in this shot the changes include a screen door with four lower sections, stone wall differs, the house numbers are bright white, and a light fixture directly over the house numbers. (00:01:05 - 00:02:20)
Continuity mistake: When Doc tells Marty, "Don't do anything, don't interact with anyone, and try not to look at anything," note Doc's red shirt design. Then it cuts to a shot of Marty as he says, "I don't get it, I thought you said this had something to do with my kids." The next shot facing Doc, as he says, "Look what happens to your son," his red shirt's design has changed, though it's the same style shirt. The same thing occurs with Doc's yellow shirt with the train design, but it's more subtle. (00:09:25)
Continuity mistake: When Old Biff drives into the garage with Young Biff in the passenger seat, Young Biff (body double) is not wearing a belt, but the belt reappears when they exit the car and Old Biff places the Sports Almanac in Young Biff's back pocket. Also, the Levi's small red tab is now missing from that pocket. (01:07:55 - 01:10:05)
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