As much as I loved the original Back to the Future, "Part III" remains a close second for me, even with it's shortcomings. I even enjoyed "Part II," although most people didn't seem to. I found the third chapter a exciting Western, which many people weren't expecting from the series.
The problems I have with the movie are with the plot holes it creates, and its refusal to fill them with what I consider to be obvious solutions.
First up is Clara Clayton. A major plot point centers around Doc Brown having to leave her behind and ultimately him having to stay in 1885 to save her life. The problem occurs in a conversation with Marty the night before they go "back to the future" - again. Marty says, "Doc, listen, maybe we could, I dunno, maybe we could just take Clara with us." Doc says, "To the future? ... No, I cautioned you about disruption of the continuum for your own personal benefit; therefore I must do no less."
He meant that taking Clara back to 1985 would further disrupt the timeline. But remember: Clara originally died falling into "Clayton Ravine." Therefore everything she does or says from that point on is disrupting the timeline. So, logically, taking her back to the future would restore the timeline, not disrupt it. She could do what she pleases at that point, and she'd only be changing the future, which hasn't been written yet.
Second up is the ending. I can only assume that test audiences hated the original ending, so Robert Zemekis decided to tack on a "happy" ending where everything is tied up nicely, but completely contradicts the events of the second and third movies! What I mean is that all through "Part II" and "Part III" Doc talks of destroying the time machine since time travel proved hazardous and that they were meddling in things that aught not to be meddled in.
So then he decides to create a new time machine, travel to the future so it can fly, and then travel to 1985 to get his dog and so that Marty wouldn't "worry" about him. Whoa there. Stop. The scientist that saw his entire life and the lives of his friends unravel because of his casual time traveling decides to create another time machine to get his pet and tell his best friend goodbye? Excuse me? I mean, I love my pets tremendously, but I'm not going to risk destroying the space-time continuum just to see them again!