Side note, but I'd dispute that the politics were well-handled, or that they were central to the films. I do agree that they were supposed to be central, but I think they were poorly done, probably because Lucas wasn't all that interested in them in the first place.
For example, we have no idea how the Senate works. Are there political parties? How does someone become Supreme Chancellor? When Valorum gets voted out, and Palpatine gets voted in, how's that work exactly? Why was Palpatine the guy who got nominated? He was just some minor Senator, no? So, what, just because the person who calls the no confidence vote succeeds in ousting the current SC, they get to pick the next one? Or had Palpatine actually shored up support and was clearly the next logical choice? We don't know, because the film doesn't say. For that matter, we have no idea why Valorum is so easily taken out of the equation. What ELSE had happened to make him ineffective? Or was it just the Naboo blockade?
And that brings up the issue of how the hell the Republic actually operates, if it can't stop one planet from blockading another. Is it like the U.N. or the League of Nations? (Which it's probably supposed to represent...) Is it like the UK Parliament or the US Congress? We don't know, because Lucas didn't care to elaborate.
When we skip ahead to the second film, we have no real explanation for the separatists' grievances, nor how the Senate is failing them. We have no idea why the Separatists want to separate, how many of them there are, nor exactly what they're separating from. It's pretty clear from the first film that the Senate doesn't really have the power to stop planets from DOING anything, so...why does the Separatist faction care what the Republic says? Why are they even a faction? We don't know, because Lucas didn't really care to explain it. Also, the 2nd film makes it clear that the Republic has no standing army. That's why it's such a big deal that Palpatine declares the formation of the Grand Army. So, without an army...what exactly does the Republic do again? It's not clear, because Lucas didn't care to explain. Probably because he didn't really have a clear idea himself.
For me, though, the biggest problem is in the final creation of the Empire in the last few minutes of ROTS. Palpatine says he's creating it and people go along with it because the Jedi..uh..attacked him and stuff. But by this point, we have no idea how the Empire is different from the Republic it's replacing. We just know it's GOING to be different...somehow. And it's gonna be bad. That's it. That's what we know.
I think the real problems with the political side is that it happens in these HUGE jumps, but the background for it is never really explored in any detail, BUT we're given JUST ENOUGH detail to say "Wait, what?! What the hell is going on here?!" That's because we're splitting time between telling Anakin's personal story, and the larger story of the galaxy (except, really, we're only telling Anakin's story), but getting very brief yet fairly narrowly focused views of the Republic in action (or in inaction, I suppose). I THINK Lucas was going for "Show them a little, let them imagine the rest." That worked great in the OT, but with the PT, I think he actually showed -- in a sense -- too much and not enough all at the same time.
I'd rather have seen Palpatine's rise to power be closer to something like House of Cards (either version). I'd rather have seen the gradual erosion of freedoms in the midst of the war. I'd rather that the Separatists were actually clear in WHY they were separating and WHAT they were separating to do that they couldn't do under the Republic. And I'd rather it have been made abundantly clear how we'd see Palpatine truly "cross the Rubicon" with the creation of the Empire, and how much worse it was actually going to get. I don't think Lucas did any of that particularly effectively, and it's why I find the political side to the Star Wars universe to be pretty underdeveloped and ineffective.