Continuity mistake: Before Griff shows up in the cafe, the Pepsi bottle's label is facing the counter. A second later, when Griff appears, the label is facing the door. (00:14:47)
Continuity mistake: When Griff pulls "Gramps" Biff out of the cafe 80's, as he swings back into the cafe notice that he swings around twice. (00:15:00)
Continuity mistake: In the Café 80's just after you hear Marty say, "It is Wild Gunman", notice the three people sitting in the second booth from the back wall. When the scene changes to Marty throwing his hat on top of the game, you can see that the people have changed tables. You can also see that they are gone again when it shows a close-up of the two kids. (00:15:18)
Continuity mistake: If you look very closely, after Marty flips on the little girl's hover board and is laying on his stomach, when he goes to get up you can see that he's wearing regular lace style tennis shoes and not the auto-lace high tops that Doc gives him as soon as they get to 2015. You may need to pause it to see them. (00:18:56)
Visible crew/equipment: When Old Biff says, "Something very familiar about all this," two crew-members are visible on the left side of Biff behind him. (00:19:10)
Revealing mistake: When Griff and his gang are chasing Marty on the hoverboards in a few shots after Marty is hanging off the back of the Jeep, when the shot shows the gang catching up, the Jeep goes through some wet places in the street, showing the camera car's tire tracks. They're not the Jeep's because the tire tracks are double-wheeled and the Jeep was not turning in that shot. (00:19:22)
Continuity mistake: When Marty is being chased by Griff's hover board gang, Marty grabs rope from a car. Just after, he has to avoid an oncoming car. One second he's holding the rope, the very next shot as he goes over the bonnet, the rope's gone. (00:19:38)
Visible crew/equipment: At the end of the famous court yard chase scene when Griff and gang crash through the courthouse windows, you can see in plain sight the reflection of cables and the mechanisms that held them in the air. [Corrected in 25th Anniversary edition.] (00:20:55)
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)
Continuity mistake: When Marty avoids Griff and his thugs by jumping in the water off his hover board, his hair gets wet. After his coat dries his hair he rubs his hand through it. It gets all messy and crazy and uncombed. The very next shot shows him talking to the girls with perfectly combed hair. (00:21:33)
Continuity mistake: When Marty dries his jacket, the clock tower pillars are in the shade. But when he hands the hover board back to the girl, they are in the sun. (00:21:39)
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 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: In the scene where the 1985 Jennifer is in her 2015 home and says "I get married in the Chapel-O-Love?" right before she picks up the picture note the Chapel-O-Love picture and frame on the bookcase behind her. After she picks it up and drops it leaving it on the floor she looks for a place to hide. Later on when the old Lorraine and George are in the living room, take another look at the picture on the bookcase; the Chapel picture is set back up. You could argue Lorraine would have had enough time to set it back up. But look at the Chapel picture; it's inserted in the frame upside down. You can tell by looking at the frame stand behind it. Meaning someone physically removed the picture and put it that way. (00:28:18)
Revealing mistake: When Doc and Marty are driving on the Sky Way Doc says "damn this traffic," but in the reflection of the DeLorean's front window there are no cars. (00:29:14)
Revealing mistake: After Old Biff steals the DeLorean, he backs it up into a dumpster and several trash bags. The dumpster and the bags move before the DeLorean touches them. (00:32:50)
Continuity mistake: When 2015-Lorraine takes the pizza out of the oven, the amount of green peppers decreases between shots. (00:33:22)
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)
Revealing mistake: When Marty and Strickland are talking in the Alternate 1985, pay attention to Strickland. Every time Marty is talking, you see Strickland moving his cheeks. He is mouthing Marty's lines. (00:42:37)
Continuity mistake: In Biff's apartment in alternate 1985, while Biff and Lorraine are arguing, he knocks her to the ground and both her shoes come off. After Biff punches Marty in the stomach, it then switches again to show Lorraine's reaction. As it does this, we see her on the floor but her shoes are back on her feet. She could have had enough time to put them back on possibly, but it seems unlikely that she would have done so as she is lying in the same position as when she was knocked down. (00:48:18)
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