Continuity mistake: When Biff and Marty fighting over the almanac while driving towards the tunnel, the almanac flies out of their hands and lands on the front windshield. Biff slowly reaches over the windshield blocking the center rearview mirror entirely with his right shoulder. Cut camera angle and the mirror is unblocked, showing Marty to the rear of the car, then a reaction shot of Biff seeing Marty in the mirror, all while he is still blocking the mirror with his shoulder.
Continuity mistake: When the DeLorean lands in Hilldale in 2015, just before it touches the ground look at the wheel nuts. They are in a plus sign position (around the black centre. However when the car lands the nuts have changed to a X shape position. The wheel nuts change to the X shape position from the plus shape in the next shot as the car lands.
Continuity mistake: Marty's hairstyle is different in the starting scene in BTTF2 to what it was in the scene at the end of BTTF (It is flatter).
Continuity mistake: When Marty gets locked in Biff's garage, we see that he can't push through the two garage doors because there's a lock on the other side. Yet, when Biff comes out to go to the Prom dance, he opens them in literally no time at all with no resistance. We don't even hear him unlock them.
Continuity mistake: When Old Biff is seen watching the hover board chase all the monitors on the wall in the Cafe 80's are turned off even though they were all on two shots prior.
Continuity mistake: When Biff is trying to run down Marty on the hoverboard, as he comes out of the tunnel there is a shot of the manure truck driving down the road. Cut camera angle to Biff missing Marty and hitting the truck, which is now at a dead stop, however there was not adequate time to do this and appears that the truck was driving then instantly stopped.
Continuity mistake: The small black pickup Marty is given at the start of this film is significantly different from the one he's given at the end of the first movie. Yet the moment is supposed to be the same one.
Continuity mistake: In the tunnel chase, watch the next shot after Biff laughs which shows Marty furiously using all his might to escape Biff. There is suddenly black on the walls around where Marty is.
Continuity mistake: When Marvin, the band member, goes to call Chuck Berry about Marty's "new sound", the telephone he uses has a black neoprene coiled handset cord. In the first BTTF, the phone had a straight, uncoiled brown cloth handset cord (seen when he says, "Well then listen to this." and holds the handset out toward the stage). This isn't because the cord was stretched out, as neoprene cords can't stretch so much that they look uncoiled.
Continuity mistake: In the Café 80's, when Griff is about to bat Marty, a woman in a blue dress passes behind Marty twice. She is also seen walking around in the next scenes that take place outside.
Continuity mistake: When Marty is in the Café 80's, there are two men talking outside on the street. Shot changes and when we go back to Marty, a second later, the two men have vanished.
Continuity mistake: When Marty is going over the lake on the hover board, at the start his shoes go right under the water, but if you look at his shoes in the next shot, they are dry.
Continuity mistake: While Marty gets to 2015 it's raining and the streets are wet, but when Griff's gang is chasing him the streets are dry.
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.
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.
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 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.
Continuity mistake: When Jen finds out that she got married in the chapel of love, her hair swaps from perfectly brushed to totally messed-up between shots.
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