Jack the Potato said:
Wouldn't it be more pertinent to talk about how a more recent franchise could be improved, like the Marvel movieverse or Twilight or something?
Honestly, even 12 years after the fact, it is still more pertinent to talk about how to improve Star Wars than Twilight. Because I can understand people caring about Star Wars. And I'm sure people talk a great deal about the Marvel movieverse. People talk about everything. Let's talk about this. And to be honest, I don't think I've ever properly discussed this, so even if it's been done to death for you, that's not true for all of us.
To deal with the actual topic,
1: Better Casting. Liam Neeson, Good. Christopher Lee, Good. Jimmy Smitts is good and I honestly can't say why he isn't used more. Ewan MacGregor is a good actor and played a good part but I don't know if he pulls off the Alec Guinness vibe, he's a bit too solemn, but that's just me. Natalie Portman is a fine actress, but a character whose primary role is a love interest has to be cast depending on their opposite number - not that she wouldn't be. It's sometimes hard to tell whether to blame bad acting, direction, or writing, but Anakin could almost definitely have been cast better, and the best way to do that would be to have had one actor through all three films, which would also him to have more of a character beyond EXTREME PUBERTY (Really, Anakin's character is just a caricature of teenage cliches), and allow the Padme/Anakin relationship to develop realistically, rather than heavily, heavily change gear in Clones. Which brings us to:
2: The Padme/Anakin relationship. I don't entirely remember, but when I saw this at what must have been the age of 10 or something, I'm pretty sure I could tell that something was off. Now that I have a more developed critical sense, I can tell that it fails on many levels. I can't be entirely sure of the writing, because I haven't seen it acted in a convincing way, but on an acting and directorial sense, it seems forced, cliched, and contrived. That needs to not happen. I don't know how it should happen, that would take more thought, I just know that it was BAD. I winced in Clones, and in Revenge it was just tacked on and silly.
3: Villains could have been used to better effect. Maul barely said anything, Grievous commits a cardinal sin by just being introduced as a bad guy without demonstrating his badguyness, and all within 5 minutes screentime of Dooku and Palpatine being their evil/conniving selves. Dooku was handled pretty well though, as was Palpatine - however with Palpatine, there was a problem in that he was the only continuous villain of the series - but he wasn't REALLY a villain - he was a scheming, puppetmaster-y, EVENTUAL villain, but the original trilogy had Vader front and centre all the time as the bad guy everyone was focused on. Maul and Grievous, and even Dooku to a point, all fill that role, but we're never really given a reason to care about them like we did Vader - all the care about the villain stuff is shunted towards Palpatine.
4: Make Jar-Jar better. In retrospect, using something like Jar-Jar Binks was something the new trilogy had to, and should have done - a CGI alien as a supporting character. Part of Star Wars' uniqueness has always been about having aliens that are very clearly not human, but act like it. In the original trilogy, we had Chewbacca along with the main group because it was essential, but he's unintelligible - which is a good thing, because to make him intelligible would either have required having a walking bear inexplicably making human noises, which couldn't be done believably, or altering the design so it was human enough to be believable, which defeated the purpose. With the advent of CGI, there's a solution - you can make an out there looking alien who can nevertheless speak and emote believably. Having one as part of the main group was essential. They just made one who was weird, irritating, and unbelievable as a character, and that's where it needed to be fixed. On a semi-relevant aside, imagine a Star Wars with BRIAN BLESSED'S Big Boss Nass instead of Jar Jar. Yes it's not a good idea, but it's a funny one.
5: Better Direction. When I think back to these films, I can imagine the same scene being done better, over and over again. That could have been more ominous, that shot could have communicated that clearer. Some of this, of course, comes down to acting and writing, but it's the director's job to manage that into compelling and effective storytelling. It just doesn't click enough.
Now, I've mostly dealt with logistical aspects rather than creative ones, because I'm not really clear on what the artistic and creative tone/direction of Star Wars is supposed to be. I first experienced it as a kid, and I enjoyed it because it was simple and cool, and in retrospect, for those reasons, it seems to be pretty much made for kids. I don't know how deep or complex it should've gotten, I don't know what direction it should've taken, because I don't know what the intent was.
The one creative gripe I'll allow myself is this: An opportunity was missed for more chill time in space. Yes, there are many scenes IN space. No, there are very few occasions where there's important character stuff going on, and where they are is quite obviously in a spaceship/spacestation. The Royal Yacht looks like an unusually styled room, whereas the Millenium Falcon Cockpit looks like it's either a very cramped submarine or IN SPACE. If there had been some decent time spent in, say, a space station above Coruscant, that WASN'T a tense situation, it would have really driven home the STAR part of Star Wars.
EDIT: I also agree with everything the post above me says.