The only problem I could see is that cut at 1:16-1:17 from Obi-Wan's thrust to Dooku's Force-push. It doesn't quite work because the eye is expecting Anakin to be in the frame from that angle (he's to Obi-Wan's right when Obi goes for the thrust, and doesn't really back out of frame.) I don't know if you could get away with some kind of silhouette rapidly moving back from middle of field to left of field, revealing the Force-push, but it's a bugger of a thing to fix...
GoodMusician: I won't go point-for-point and rehash what's already said above. This is a really, really nice piece of work. I say that because I don't want to seem like I'm doing nothing but criticising -- this cut does work a hell of a lot better than the original. So dealing with my nitpicky stuff...
(1) "Your swords please." Always annoyed me right from the word go, since they don't actually have big shiny bits of metal (well, not the parts that're meant to hit people, anyway.) And Dooku has referred to lightsabers by their correct names in the past -- on camera, during Ep 2. Think it might be possible to steal the word "saber" from that and sub it in for "sword"?
(2) Not sure if there's much that can be done about this, but it's the same issue as with CommanderCourage's edit -- the cut between Obi's thrust and Dooku's Force-push. And on fullscreen another problem emerges. In the shot before the cut Obi-Wan's still moving towards Dooku. In the shot after he's not; he's standing still. The eye notices it even if the mind hasn't got time to register it. Maybe Obi's stillness can be solved by the ' silhouette' of Anakin in the shot, I don't know...
(3) The shot right after Dooku's hands come off (IMHHHO) needs Dooku's reaction back in it, if only for a few frames as he starts to drop. There isn't quite enough time for Dooku to go from standing to kneeling for Anakin to do what he does in this edit, to my eye. If Dooku has a brief second or two's reaction, Anakin's got time to pick up and cross the sabers. But otherwise I really like the ' no thinking' way that Anakin ends the duel -- it's in keeping with Qui-Gon's old advice " Feel, don't think," and is much more evocative of an Anakin who got carried away in the heat of the moment.
(4) Pity about no lip movement when Palpatine's laughing. Rotoscope it, maybe, or 'jiggle' the head a little?
Again, other than those things, it works really well. I also noticed a certain 'quickness' to the way Palpatine says "It is only natural", but I think it might be coming from the mismatch in the "background hum" of the shots before and after that line, not necessarily because it's too quick a line...?
Just quickly on the leadup to it, though ... I think honestly there's enough room to eliminate the "Artoo does flamethrower" thing, even if it takes removing the entirety of the elevator-stop sequence. Or at least take out the part where Artoo's actually discovered, if possible?