I realize that so much of this sort of discussion comes down to taste, but I don't understand how AOTC takes as much flak as it does.
TPM was an utter failure in most respects, but it did at least succeed at getting the PT story underway. A lot of AOTC was significantly flawed, but we did get to see Anakin struggling with his mentor, with his attraction to Padme, and with his Dark Side temptations (I disagree with the execution, as I will address later). ROTS doesn't fulfill its primary purpose - a plausible turn to the Dark Side by Anakin Skywalker.
First of all, Anakin's character development was out of its logical order. In AOTC, Anakin openly clashes with his master but is all buddy-buddy with Obi-Wan in ROTS. If someone is moving gradually toward the Dark Side of the Force, does it not logically follow that Anakin would be more friendly to, and less critical of, Obi-Wan the second movie rather than the third? Ditto his attitude toward the Jedi Order. He doesn't particularly praise or criticize the Order until they placed him onto the Council without granting him the rank of Master. I actually liked that plot point in ROTS, but there was absolutely no build up to it. Anakin, starting in AOTC, should have been wary of the Order and that suspicion should have festered and grown all throughout AOTC and ROTS up to the Council's decision, where Anakin's distrust of the Order reached a boiling point. Anakin at least revealed a mistrust of Republic politics in AOTC, but that one aspect of Anakin's character wasn't enough to convince. I know lots of people who don't trust the government and don't slaughter children.
Second of all, Anakin's treatment of Padme in ROTS was baffling. "I love you, I love our child, I'll save you, but right after I turn to the Dark Side, I'll try to kill you after we have a little spat just because you're hanging out with Obi-Wan." Huh?
Third of all, Anakin's loyalty to Palpatine should grow steadily (again, starting in AOTC). No one kills children ten seconds after swearing loyalty to another - hell, I'll bet even Charles Manson gave his followers simple tests at first: "Prove your loyalty to me...and hand me that pencil!"
ROTS was supposed to be the payoff of the PT - but it didn't work for me.