Talking of costumes, it makes me think of the decision to have the Jedi wearing Tattoine robes; a fairly big mistake, I think.
Lucas was keen that audiences would recognise the Jedi as soon as they saw them, but I think he should have have a bit of faith in his own scene-setting skills, and in the audience's intelligence. In the end, this detail doesn't match up with the OT, even though Lucas was keen to have it all blend together. Maybe we wouldn't have had quite so silly Jedi haircuts either (but I won't go on about that again!).
Likewise, returning to Tattooine so that it "looks like Star Wars" was also a mistake - part of the "tiny universe where everything significant happens to the same small group of characters" problem. We should have had new, unique locations - Anakin shouldn't have grown up on Tattoine. Jabba shouldn't have been in it, etc.
I realise Fett was always connected to the Clone Wars, but he shouldn't have been in it as a child; better to change that bit of back-story rather than put in lame fan-pandering stuff that harms the character (although I did like the Jango-Kenobi fight; one of the few decent fights in the PT in my opinion). Other similar errors were having Chewbacca know Yoda, Anakin build 3PO, etc. All this stuff harms not just the PT, but the OT and thus Star Wars as a whole. You end up not just with one lousy film, but damage to the decent films in the series.
And if you're going to have lots of lightsabre use, spend a bit of time making sure the extras don't look inept/stupid holding them. I'm thinking of the minor Jedi in the arena battle (stupid poses and moves abound, even by PT standards) and the children in Yoda's classroom, who apparently would rather be doing anything rather than learning how to move a sabre. It all just seems so half-arsed. I know Lucas put a lot of effort into the PT, but a lot of it has a "that'll do" type feel.
Most of the above is "what they shouldn't have done", rather than "what they should have done", but I think avoiding the above would have at least helped the films get on the right track. In essence, it's about having a lot more faith in the SW universe, and not having to namecheck existing stuff ("hey! remember Chewie? here he is!" type of nostalgia). What we got was a peculiar kind of nostalgia-pandering that damaged the original thing you're meant to be feeling nostalgic about. There was already enough connection to the originals - Kenobi, Vader - we didn't need to see a prototype/young version of absolutely everything.