In terms of major plot points I'd change, the main thing I'd do is age Anakin up so he is an adolescent in the first film and maybe 30 when he turns in the third..
For mine the prequels should have been a love triangle with Obi-Wan and Anakin looking for Padme's affections.
Then it makes the descent of Anakin all the more tragic as Padme would have chosen him, only for him to kill her and Obi-Wan is left with the kids from that union.
Spot on with this.
Ep 1 should have started out with AOTC aged Anakin.
I didn't mind the pod race but that is where the movie should have started and without any Trade Dispute, Jar Jar or Jedi interference; start with a young Anakin building his own pod race to try and buy his own way to freedom. Immediately we have a protagonist we care about and an action set piece that is actually relevant.
Perhaps have him as a massive underdog who loses, but in the process catches the eye of Obi-Wan who befriends him seeing his skill and ambition, and pulls a few strings to get him into the Pilot Acadamy where Obi-Wan is also training to be a pilot. The Acadamy should drive the movie from here, not that boring unengaging political drama. Anakin (and us) would also naturally be blown away by the world building such as Coruscant.
That's also where you'd bring in the Padme character, juxtaposed with her and Obi's privileged backgrounds with Anakin's humble one - and also separate the two leading men by making Anakin impulsive and rash but with incredible piloting skills and that Han Solo roguish charm, while Obi is more level and pragmatic and obviously the 'safe' bet.
Keep lots of tension between the three, but she won't make a choice until AOTC.
Obi-wan could then introduce Anakin to the cultish Jedi which runs in the background, Anakin again being a natural with the force, seduced by it and on starting the path to becoming a slave to it. That would be when you'd bring in the political backdrop and introduce the father figure characters of Mace (immediately threatened as this brash kid is force strong - no midichlorians), and Palpatine who also sees this but takes on a sympathetic role for the ulterior motives we already know. Sort of like Platoon but even less black and white.
The climax of episode one could have worked - no gungans vs droid army but a space battle followed by a saber fight would have been just fine.
No Qui-gon - utterly pointless character.
No Yoda, at least not for ep 1 - that was crappy fan service
Get Dooku in early, he works well as the fallen Jedi, chasing absolute power with a mysterious leader behind him. He could even be Obi Wan's master, furthering Obi's character with him choosing the 'good' side.
Maul is fine as a black box villain - serving to showcase Anakin's power and/or anger, or used as a pawn the way Dooku was.
.... haven't really thought about it much after that, but that's how I'd go for episode 1 at least.
I thought eps 2 and 3 had decent enough plots but suffered from not having the backstory and character development as it's foundation.