Audio problem: When the kids are watching the Dr. Dre and Eminem music video on TV, you can hear the song disappearing and reappearing in the background. Some parts of the song are heard multiple times. Plus when you hear the music off screen the "bad words" aren't edited out, like they are in the shots with the TV screen.
Continuity mistake: When Marty and his girlfriend are laying in bed together after engaging in physical relations, Marty lights a joint. It starts off small, but when his girlfriend smokes it then passes it back to him, the joint is longer.