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: Throughout this movie and Part III, whenever there is a special effect, like two Biffs in one scene, the scenes with the flying cars, and basically whenever an actor is playing three or four roles at the same time, if you look very carefully, you can see the picture flash ever so slightly repeatedly. It looks almost as if the picture is throbbing a bit. Might be more visible if viewed on the DVD.
Other mistake: A book that thin would not be able to hold even one year of statistics of all sports at the detail level purported in the film. When we see the pages (for example in the tunnel, when the book is in the wind screen of the car) we can see that the font is quite large, and there are even text sections - it is not all tables and numbers. And it can't just be regional results, since we hear about a college football match, which is listed in the book.
Continuity mistake: When Marty and Doc find Biff's car, Marty is not present in the DeLorean, but he appears in the next shot. (01:29:54)
Visible crew/equipment: When Marty realises that the almanac is not inside the dust jacket, a set light can be seen on the far right side of the screen. It can also be seen when he realises where Biff is. (01:21:08 - 01:21:45)
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 the police car arrives in Hilldale, there are no door handles on the car, but in the next shot, some appear. (00:27:16)
Continuity mistake: When Marty hides in Biff's car as he walks over to it after leaving the auto shop, the left visor on the car is raised, but in the next shot, it is lowered. (01:05:53)
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)
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)
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)
Continuity mistake: When Marty sees his dad punch Biff, he sees his other self standing near the group of people. He pushes between a guy and his date with nobody behind them. In the first film, there are more people behind them that Marty had to push through.
Audio problem: When old and young Biff listen to the end of the football game in the car, as the two are talking back and forth about how old Biff knew what the results would be, the sound of the announcer on the radio lowers and then suddenly disappears altogether... yet neither of them physically turn the radio down or off. The two are shown the whole time talking to each other and both their hands are away from the radio. (01:09:39)
Continuity mistake: When Doc and Marty arrive in 2015's Hill Valley the flying DeLorean (a scale model) is missing the key lock and door handle dent. When it lands (and swaps to a real car) both appear.
Revealing mistake: When the movie begins and the car takes off (achieved with a scale model car) note Doc's stiffness and fuzzy hair, revealing he was replaced by a dummy.
Continuity mistake: 1955-Jen is showing some dresses to a friend when Biff shows up. Watch the man passing by the girls. He walks by twice.
Continuity mistake: Inside the tunnel, Biff punches Marty who's on the hoverboard, launching him back. A shot later Marty is suddenly standing tall and next to Biff, and gets punched again.
Continuity mistake: When 1955-Marty reads Doc's 1885 letter next to the Western Union car, his right hand is either on the lower part of the paper or the upper, depending on the shot.
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)
Continuity mistake: When 1985-Jen encounters her old self, 2015-Jen walks several steps further. When the angle changes, old-Jen has stepped back 4 meters to allow for both to stare at each other closely.
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