Back To The Future 2 - Temporal Back-Talk
I don't believe this has been addressed in an actual Slip-up, so forgive me if I'm wrong in that.
The Doc clearly explains after they return to Alternate-1985 (or go there for the first time, as things are) that if a person travels back in time, changes something, and returns to the period they left, they will have altered the world as they knew it.
This is quite evident in that when they return, Alternate-Biff is the corrupt ruler of their town--a major change in the scheme of things.
However, there's a slight problem with the events that lead up to this situation.
Old Biff steals the Time Machine, travels back to 1955, and gives his past-self the Sports Almanac. After, he takes the Time Machine and returns to his own time, so that he can replace the car before it's missed--which allows Marty and the Doc to go about the rest of their adventure.
The problem with this is that it's not plausible. If Old-Biff gave Past-Biff the Almanac, that would have instantly begun the series of events that created Alternate-1985. So, when Biff returns to the Future, it would've been Alternate-1985's future... Not the one he left.
What this means is that everything from that point on in the movie, and in the last movie, are based on a flawed concept of which the entire movie is based.
If you disagree... Feel free to dispute my argument, as I'm sure many will from what I've seen here.
Just the movie itself