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.
Plot hole: When Old Biff goes back to 1955 to give himself the almanac, he comes back in the Delorean to the version of 2015 that he left, not the other, skewed version in which he is rich. Everything in 1955 should have changed around the Doc and Marty, as the Doc tells Marty everything will change around Jennifer and Einstein later on in 1985, when Marty and the Doc go back to restore normalcy. George is alive in this future, so we know the skewed version hasn't taken hold.
Suggested correction: It is established in the movies that the effects of the timeline being changed are not immediate. For example, in the first movie, in the photo of Marty and his siblings, it takes some time for them to vanish from it. When Doc tells Marty everything will change around Jennifer and Einstein when the timeline is restored, I don't think he meant the future will be restored to normalcy right that second, but more after an ample amount of time has passed for everything to be right. After Old Biff gave the almanac to young Biff, there was ample time for him to return to the original 2015 before it changed into the alternate 2015.
That would mean when they restored the timelines it would have taken time for it to adjust again, but it didn't. The new timeline was created but the old one remained because Marty and Doc were still in the original future. However, even though they are not in their original timeline it doesn't make sense for them to still be there, the timeline should have been erased or else old Biff wouldn't be erased either. Again though, a copy of another plot hole, which one is the oldest and original?
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: At the start, the DeLorean hits the left dustbin and comes to a halt. At the other side of the street, there is only one car parking near to a house. From another angle there's a different red car parking on the other side of the street, and the tree that stood between both houses has gone. (00:01:15)
Continuity mistake: When Doc drives Marty up behind Biff, just before they enter the tunnel and Marty grabs Biff's car, you see Doc acknowledge Marty and then turn off left, but as the camera pans back you see the car veer to the right. (01:30:45)
Continuity mistake: When Marty is at the dance in the first film, the room that the band leader rings his cousin from is on the right, but in this film the room is on the left. (01:26:09)
Continuity mistake: When the rain stops after Marty and Doc first get out of the DeLorean in 2015, Doc looks up at the rapidly clearing sky. Directly above their heads the sun is shining brightly. However, if you look at the tops of the buildings you can see sunlight hitting them from the sides. I suppose we will have another sun by 2015? (00:06:42)
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.
Revealing mistake: During the tunnel chase at the end of the movie, in the shot shown from the ceiling of the tunnel, you can see in the shadow of the hover-board, skate-board wheels.
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.
Visible crew/equipment: When Doc, Marty and Jennifer are going to leave 1985 (at the beginning of the movie), the camera is reflected in the back part of the car.
Revealing mistake: When Biff steals the DeLorean and flies off with it, the DeLorean disappears just before it reaches the top of the screen. It appears to just wipe out of frame before it's supposed to. This mistake is visible on the Netflix version.
Visible crew/equipment: After Marty runs away from what used to be his house in the alternate 1985, he walks towards a crime scene. There are two instances in this scene where you see the shadows of the camera and camera operator passing by on Marty's t-shirt.
Revealing mistake: When the hovering object walking the dog in 2015 flies by, a moment before it disappears, you can see the wire used to support it.
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.
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.

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.