Sorry I'm rather late to the game, but a few thoughts...
Not sure how possible these suggestions would be... Apologies also if this is long.
General observation which I think we would all agree on of the prequels is there is far too much pointless exposition and not enough action. Anakin/Vaders transition is too quick IMO and no Jar-Jar...
It also seems to me the plots also don't make sense, for example why on earth would the Trade Federation want to invade a backwater planet like Naboo?
My first suggestion would be to make Naboo have something unique and valuable, perhaps a new power source that has just been made/invented there... One that would allow the construction of much larger capital ships space station and also a significant upgrade in weapons capabilities i.e. a superweapon. It could be secret, but as Palpatine's home planet he would be privy to that information. That would be a reason that both a Sith Lord and a massive company with military assets to have an interest in Naboo.
Ironically the Charachter/relationship I think that needs to be changed the most is Yoda and Obi-Wan... "Yoda the Jedi Master who trained me". So shouldn't Yoda be Obi-Wan's master. Seems there could be several solutions here, either have Obi-Wan already a Jedi Knight. Or have a seen where Yoda hands him over to Qui-Gon because Yoda is stuck at the temple teaching and wants Obi-Wan to go on some missions.
There are several other key changes I think that should be done to Characters. Firstly I'd suggest making Padme, a Princess instead of a Queen (she's 13 after all) and also remove that election nonsense, who elects 13 year olds?
Then also make Anakin much older than in the TPM... I'm going to continually use the words more sense here... I'd suggest having him between the age of 13-18 - romance between him and Padme would also make much more sense, the council moaning about his age would make more sense... And him being a crafty pilot would make more sense. Deffo make him blow the Trade Federation ship up deliberately + more of him being an awesome pilot.
Tatooine needs major work, it lags and is boring. I think a lot could be cut... There needs to be some sort of meeting with Anakin, perhaps him saving someone being mugged, or Qui-Gon see's his podracing abilities. Interesting touch could be to have Anakin having already constructed himself a lightsaber...
I think during this time a romance between Anakin and Padme would make a lot more sense. A lot of what I think needs to be changed is in the first sections of the film... Though the space battle being made better and having Anakin be a much better pilot would be great.
I think it would also be best for the Phantom Menace to end with the beginning of the Clone Wars... i.e after the Trade Federation is defeated they form an alliance with others and go to war with the Republic... With Darth Sidieous pulling those strings.
Finally; I'd really like Dooku to be in TPM, possibly as a Jedi prior to leaving the Order (perhaps even see him leave the order because of Qui-Gons death).
With the Clone Wars having already begun, we would then be right in the middle of them for Episode 2... I think it would be good to see Grievous killing Jedi during the second film to set him up as a threat. Episode 2, instead of being a romance film, would be a film following characters exploits in the wars. Think there should be more of Anakin piloting again...
Here's another point it's called the CLONE wars... Shouldn't that mean it's Clones vs Clones rather than droids? However not sure how possibly it would be to change that, but just a thought.
Anakin's decent to the Dark Side, perhaps would make a bit of sense if he does gradually more morally grey things to defeat the separatists... If anyone is familiar with KotoR in a way similar to how Revan slowly gets darker over the course of the war with the Mandalorians.
The final push I think could be Sideous framing the Jedi for killing/being to blame for Padme dying (she doesn't have to be dead, just Anakin think she is)... And then Anakin raging and killing the Jedi over what has happened...
I'd actually like to have seen Darth Vader in suit hunting down Jedi... Anyone else think thats a good idea.
Anyways I will stop boring you all with my small 2 cents on the Prequels...
