Continuity mistake: When Marty (the Marty wearing the dark clothing) is at the dance and the Marty of 1955 is on stage is about to sing Johnny B. Goode, you can hear the 1955 Marty saying "this is a blues riff in B, watch for the changes and try to keep up" through the microphone. Yet in the original, Marty looks away from the mike when he says this and is unamplified. The quote is different as well. He says "this is a blues riff in B, watch for the changes and try to keep up" in part I, but in part 2 he says "this is a blues riff in B, watch me for the changes and keep up, OK?"
Continuity mistake: In the beginning when Doc takes Marty and Jennifer to 2015 for the first time, they are descending towards Hill Valley. Doc turns the steering wheel to the left but the car goes right and down.
Continuity mistake: When Marty is in Mr. Strickland's office trying to take back the almanac, it shows a wide view of the office with two flags right next to each other. After cutting to a close up view of Marty they are apart, then Marty moves them together.
Deliberate mistake: When Old Biff and Young Biff are sitting in Biff's car, the car's rear-view mirror vanishes during all shots of Old and Young Biffs together. Presumably this made the split-screen effect easier to do.
Continuity mistake: In the part where Marty is trapped in Biff's garage, Biff's rear view mirror on his car is at the very top of his windshield. Later on when Marty is holding on to the car with the hover board the rear view mirror is in the middle of his windshield. The rear-view mirror was lowered about six inches or so.
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.
Continuity mistake: Notice Marty's hair in the scene when he's playing "Johnny B. Goode." It's quite larger than when he says, some seconds later, "I guess that you're not ready for it yet." That's because when he says that, it's a recycled shot from the original BTTF, whereas most shots showing he's playing the guitar are newly made for BTTF2. However, Marty's hair is considerably longer in the new shots.
Audio problem: When Doc and Marty return to the year 1955, you hear the squealing sound of tyres braking heavily, but the DeLorean is flying.
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.
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.
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.
Continuity mistake: When Biff is trying to get Lorraine to go to the dance with him, (the bit when Lorraine is looking at her dress) you see the same extra walking past her about three times.
Revealing mistake: When Doc and Marty arrive in 2015 when the car is landing in the alley you can see the mechanism that is lowering the car. Just as the scene switches from the front of the car (right after the headlights go out) to the back of the car, look between the car and the building at the same level as the back bumper. There is something that is moving down with the car.
Audio problem: After Doc and Marty return to 1955 in an effort to steal the almanac back from Biff, they land the DeLorean. Doc says, "Here's some binoculars" then says "and" but watch his lips as he says "and", it just doesn't match. You could argue that it is a bad angle but even at the angle it's at, you get an OK view.
Plot hole: When the "old Biff" steals the time machine in 2015, as Doc and Marty attempt to retrieve Jennifer, it shouldn't be possible for Biff to return to the world that exists around him, as he gets out of the car back in 2015. Doc, Marty, Jennifer, and the world around them ALL should no longer exist, while still trying to escape from 2015. An alternate time line should have been created the moment "old Biff" left 1955. (Thus, Doc's explanation to Marty via the chalkboard explaining an "Alternate Reality"). This all started in 1985, and one result of old Biff's ventures, we learn that Doc is committed to an institution and couldn't even invent, or at least complete, the time machine by October 26th, 1985, which is the starting date of the initial film.
Visible crew/equipment: When Old Biff says, "Something very familiar about all this," a crew member is reflected in the restaurant window behind him.