Continuity mistake: In the first movie at the dance, he plays the guitar quite horribly before his parents kiss. In this movie, there is a shot before they kiss and Marty is playing the guitar perfectly.
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)
Continuity mistake: After George knocks out Biff, Biff has an obvious contusion and blood on the right side of his nose and mouth. As the hoverboard chase scene progresses over the next several minutes (particularly in the lighted tunnel), the contusion and blood repeatedly disappear and reappear on Biff's face from one camera cut to the next.
Continuity mistake: At the start of the movie Biff is waxing George's car in the driveway with his truck parked next to it. However it completely disappears and isn't seen again even though Doc appears and parks where Biff's truck was, and Biff doesn't leave the premises.
Continuity mistake: Marty's new Toyota truck in the garage at the end of Back to the Future and beginning of Back to the Future Part II has different front license plates. In the first movie it's 2EZP916 then it's changed to 2BAK860.
Factual error: When Biff and Marty discuss the Almanac in the Alternate 1985, a magazine is visible. This is the March 1989 issue of "Mustang." (00:57:05)
Continuity mistake: At the end of BTTF 1, when Doc tells Marty and Jennifer that they have to come back with him to 2015, while they are sitting in the DeLorean, the Doc says," ...where we're going we don't need (pause) roads," and as he says "roads" he puts his silver glasses on normally. But in the beginning of BTTF 2 in the same scene, when he says," ...where we're going we don't need (pause) roads, he swings his glasses on really fast with only one swish as he says "roads." (00:02:23)
Continuity mistake: When Marty is reading the letter from the Western Union man, he's standing with the letter in front of him at chest level. Switch to side camera angle and he is now bent over, holding the letter down to the car's headlight. Switch angle again and he's standing up again, with the letter back in front of him.
Continuity mistake: When Marty's on the hover board on the lake, watch the Clock tower's entrance behind him: Depending on if it's a wide, medium or side shot, the number of guards change from one to two, or one that runs away but suddenly appears back in place.
Continuity mistake: When Marty is playing his song on stage (during the part where he knocks over the speaker) the music playing is at a different stage to what it was in the first film. The music is now a few seconds ahead.
Continuity mistake: We see Marty putting on his right Nike boot but not his left. The camera cuts from his feet to his face saying "power laces, all right" then back to his feet, now both boots are on. (00:07:45)
Factual error: In 1955, Doc says "Sunrise should be in around 22 minutes." This wouldn't be possible as the sky is fully dark (except for a slight bit of light on the other side). If only 22 min from sunrise, even on a stormy overcast morning, the sky would be fairly light by then.
Continuity mistake: At the end of the first film when Marty leaves the garage to greet Jennifer, he does not have a watch on throughout the whole scene. In the identical scene at the beginning of this film, Marty is wearing a black watch.
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: At the beginning, when Marty is examining his truck in the garage, the left side of his shirt is tucked-in in the front, but in the first film, Marty's left shirt tail was hanging out. (00:00:36)
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.
Visible crew/equipment: Just as Griff is about to crash through the front door of the court house after he is chasing Marty on the hover board, you can see someone (the director?) on some sort of crane in the reflection of the glass. (00:20:58)
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