Well, it's hard to improve upon a series as solid as Firefly, but given its short but very sweet run, it didn't have much opportunity to jump the shark. This post is likely going to be fairly short, too, since I don't think I can come up with a lot of stuff I'd redo. However, since the show was too good to last, feel free to post what you think would interesting directions for hypothetical episodes to move in.
The Movie: Serenity: My main complaint is that it felt artificial, inflating the crew's importance. Exposing the Reaver origin and spreading the word across the solar system(s) felt kind of like shoving the crew into a typical Hollywood B plot, rather than flow naturally. The characters were handled well enough, and the Operative was a good adversary, but they could have figured out something else to do with them. One angle I think I would have preferred to take would have having him as one of the Hands of Blue going after River, or maybe a rival of some sort for Shepard Book.
And I'm about tapped out already.