Sorry, Jarod. The BACK TO THE FUTURE movies are riddled with problems, too, although they are a lot of fun.
By logic we can assume there are two basic universe types. (There may be more that I haven't thought of.) The "single history" universe is the grandfather paradox type. That means one cannot erase the causes of events. For example, if you go back in time to fix some problem, you will eliminate the reason for your having time traveled. See my above post for some of the fallacies used to side-step this.
The other model is the "multi-verse" type, where every possible juncture spawns another universe. If something can happen in two possible ways, it happens both ways, but we are aware of only one.
The first BTTF assumes the "single history" model, then proceeds to violate it several ways. Also, why would it take a whole week for Marty to start vanishing? This assumes time is nested within another time dimension. Despite keeping his parents together, Marty has invoked paradoxes: Lone Pine Mall, remembering that his parents told him a story about grand-dad hitting George
with the car, etc. The only way to save the first movie is to assume a multi-verse, but then nothing Marty or any of his analogs could do would result in one of them vanishing. Anyone "changing" time would simply spawn another universe.
In BTTF2 Doc explains alternate timelines, then violates it. Jennifer passes out and is left on a porch in an alternate 1985. As Marty and Doc prepare to jump, Marty asks, "What about Jennifer?" Doc assures him that she will be fine when time is corrected around her... In reality, Doc just abandoned Jennifer from one universe in an alternate universe that they will never return to.
I could go on, but you get the idea. "Paradoxes" are fine in fantasy stories, however. Then they become wishful thinking on how some event might have been, if only... I've heard some people call GROUNDHOG DAY a time travel movie, but it is more of a karma story. So a deity is involved and no business of "science" fiction.