The Phantom Menace:
It needs more than an axing of midis and less Jar Jar. It needs less people standing around and talking for one thing.
It also needs a driving narrative that takes us from one location to a new one and then another new one, and so on. It needs a forward momentum to it. TPM just stops in places: the jedi on Naboo take forever to warn the Queen, the loooong podrace, and parts of Coruscant drag. They could all be trimmed.
I'm also for preserving OT characters for their proper first appearances like the Tuskens. Reducing them to comics in their first appearance in the saga diminishes their threat later in ANH. Same with Jabba.
Make Tatooine something different for TPM than what it was for the OT. Set up things. Add some history and deeper meaning to what we will see in ANH and just accepted at face value.
Maybe it was a world ruled by a gang of criminal slavers led by Watto that Qui-Gon bankrupts in the podrace bets, leading to the rise of the Hutts to fill the void?