You didn't find his fall believable? Odd, to my mind, that is EXACTLY how you fall.
There's an obviously contradictory web of lies that the emperor weaves, yet Anakin buys into it (this is also believable: remember Korihor? YEah, the one that tells ALma that an angel from God appeared to tell him that there is no god? Yeah, but he still bought into it). Anakin is THERE because he needs to save Padme, it's more important than all the problems with the council trusting him, it's more important than killing an obvious source of evil. He's made a conscious decision to join with Palpatine, KNOWING he was a Sith lord. It was more importnat to him than anything else. He's still horrified with himself, but he has to do it to save Padme. And as he sins more and more, he starts to accept other of his ambitions being important too.
Babies? Yeah, they were too big, but I would think considerably less of the mother that let her 1 month old be used in a film if she wasn't the one holding him. THat didn't bug me in anyway.
The only problem I had with wookies was that they were built up so much for movie promotion (which, frankly, is probably a problem with the fans more than Lucasfilm, we saw wookies, we wanted wookies, we got hyped about wookies...). The only thing that was necessary about them was that it had to be SOMEBODY. Why NOT be wookies? So it didn't really bother me. True, there's nothing to indicate that Chewbacca was a war hero, but there was also nothing at all to indicate that he WASN'T. The clone troopers are hunting down and wiping out wookies in the last scene on Kashyyk. If Chewbacca was a war hero, that makes him even more of a loner refugee in the galaxy by Episdoe IV. And he *is* 200 years old, so sorry boys, that was Chewbacca the buddy of Han, not his dad.
Things that bothered me? Not much. Perhaps Palpatine's butt-crack forehead, but that's about it.
I find it kinda funny that eight limbs (plus 3 heads, not counging battle droids) get severed over the course of the flim.
The thing I liked most? Seeing the Millenium Falcon. Yes, I swear I'm telling the truth. I'm the only one I know that recognized it, but I double checked on the second viewing. It was there.