2 is the worst by far. The clumsy introduction of Marty's alektrophobia, the dystopian darkness of the alternate present that is tonally dissonant with the entire rest of the series, the terrible old age make-up, Michael J. Fox as his own children inspiring a million Eddie Murphy and Martin Lawrence vehicles, the list of atrocities goes on.
I think the worst is the time travel completely falling apart though. BTTFs 1 and 3 are more character driven, but BTTF2 is specifically about time travel, so it's kind of important for it to make sense. How did Old Biff get back into the old future after he changed it? You'll note I didn't ask why, because why is obvious: The main characters needed the time machine. Old Biff's time paradox is small potatoes compared to the major issue in BTTF2, though: Future Marty.
In the BTTF2 future timeline, Marty McFly, his girlfriend, and his disgraced scientist associate disappeared from 1985 and weren't seen for thirty years. So who the fuck is this future Marty? And future Jennifer? And why are their children clones of Marty? Is the McFly household being invaded by Skrulls? Why didn't Doc just ask future Marty to help out? It's the same character and you wouldn't need to risk two Martys colliding and making space-time collapse in on itself. For fucks sake, BTTF2.