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?" (01:24:25)
Plot hole: If Old Biff changed his past and went back to 2015, he goes back to HIS future, not the bad future, but Doc later tells Marty that if he were to go to the future to stop Biff from taking the almanac, he'd go to the bad future, so Old Biff technically shouldn't have been able to return to "his" future at all.
Trivia: When Marty discovers that he is in an alternate Hill Valley, there was going to be a scene with him discovering that his sister Linda was a prostitute and his brother Dave a homeless drunk living on the streets. These scenes were scrapped as Wendie Jo Sperber, who played Linda, was pregnant at the time.
Plot hole: After Biff steals the DeLorean and travels back to 1955 with the Sports Almanac the movie states that he creates an alternate timeline. Doc Brown does a good job of illustrating this on a chalkboard. So if, as Doc Brown states, Biff created an alternate timeline, then when he travels back to 2015 it would be the alternate 2015. Even if the original timeline stays intact with Doc and Marty in it, they'd be trapped there because Biff took the Delorean and returned it to the new timeline, not the one they're in.
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.