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.
Plot hole: They go and buy Anne Marie a whole new wardrobe. So, how come in the remainder of the movie she continues to wear her old rags?
Suggested correction: The effects of the past being altered may not have happened immediately. It is possible that it took time for the timelines to adjust to the changes of events, meaning enough time would have passed to change 1985 when they return, but not enough time could have passed to change 2015. By the time Doc says if they went back to 2015 they would be going to an alternate future, some time has passed, so the effects of the past being altered and taking ahold in 2015 and altering it are more likely to have occurred by then.
Casual Person
Here is what you say: "perhaps it took time for the time lines to adjust." What kind of time would timelines take? Time is time, it doesn't take time to change the timeline. That doesn't make any sense. Some people claim it was the DeLorean itself that came back to its own original timeline and only then reset itself in the new one, but then the new timelines being erased later on wouldn't have happened either. So its a genuine plot hole.
lionhead
It's established in the first film that it takes time for the changes to take effect. Marty and his siblings slowly disappear from the photo, rather than instantly. Although the scene in BTTF2 was deleted, it was filmed showing Biff dying and slowly fading away after his return to his present.
Yet they were restored instantly without any outside influence at the end of the movie. There are a lot of things wrong with this movie and the first one. Old Biff disappearing should mean that Marty and Doc should slowely disappear as well, even the DeLorean. But they didn't, that doesn't make any sense. The point is there is a plot hole, somewhere. To know where all you can do is look at it logically and then you automatically come up with Old Biff going back to the future but not the alternate future. If he did there wouldn't have been a movie, but that's the plot hole.
lionhead
The timeline didn't change until he made his first bet which was some years I think after receiving it. He immediately travelled forward after giving the act, meaning he will still jump forward to the original future.
The timelines would instantly change, and Old Biff couldn't possibly have returned to "normal" 2015. It's just a poorly-thought-out time travel plot hole (or a deliberate error to expedite the storyline).
Charles Austin Miller
Suggested correction: In context, Doc was saying that they couldn't return to 2015 to stop Biff from stealing the time machine, because Biff didn't steal the time machine in the alternate 2015, he only stole it in the original 2015. Marty and Doc didn't stay long enough in 2015 after Biff returned, and that's why they didn't see any differences. Also, though they were unaware of it, Biff was dead in the alternate 2015, so the disasters he caused might have reverted back after his death.