Alright guys, you're explaining how it can be better, not why on its own Anakin's fall fails. I already explained why I feel it is believable, and replied to what Frink wrote, though I have to admit the last two points Frink wrote are very true, I am keeping them in mind...
Let's examine what's presented to us and if it works on its own, not compared to an alternative. By the way what I write below is my thought process so if you encounter wonderings or changing of opinions, you know why.
The Jedi of this era are hypocritical, reckless and corrupt beaurocrates. Their code is that they forbid love, passion, attachment, fear, anger, hate... Basically emotions people feel all the time. But they bend their own code which is not even perfect in the first place. The only exception to this rule is Qui-Gon Jinn. He is a compassionate, soft, caring, ideal father figure. He is exactly what a Jedi should be. So no Moe, he is not reckless, whatever made you think that? Contrast that to Mace Windu, who is exactly what the Jedi are at that moment: Careless, corrupt hypocrites, who act angry and hateful from time to time.
Anakin was presented to us in The Phantom Menace as a young, innocent child, simply because GL wanted to convey Anakin's fear of losing his mother; and this does set up Anakin's fall to the Dark Side. In fact, the council sensing he has this fear of loss, and Yoda explaining how this leads to the Dark Side (Fear -> Anger -> Hate -> Suffering), sets up Anakin's fall throughout the trilogy.
This is significant because the supposed protectors of the galaxy never even bother to free his mother. So when the visions of her mother kick in, and Anakin rushes to save her but fails, he begins his anger and hate, towards both the Tusken Raiders and the Jedi. This is one of the many things that Anakin's fear of loss causes.
Another factor that is important with Anakin's fall is that he is held up with super high standards (i.e. The Chosen One prophecy). Palpatine keeps saying he'll be the most powerful Jedi in existance. All this is there to get Anakin's arrogance up to maximum level.
I brought up Qui-Gon Jinn earlier because he was the perfect person to train Anakin. He would have taught him to control his emotions rather than surpress them, and also stay humble and compassionate, caring. He would have been much better than Obi-Wan, who is inexperienced and conservative. Unfortunately, Qui-Gon dies, still believing in Anakin, and he is stuck with Obi-Wan. The reason for the fights Anakin and Obi-Wan have in AotC is precisely because Anakin becomes arrogant. It is Obi-Wan's failing that he is not a humble, compassionate guardian. Also Palpatine constantly holding Anakin to a high standart, and exposing the corrupt views of the Jedi makes Anakin's hate for them and his own arrogance grow.
Anakin's fear of loss comes back bigger than ever when he recieves a vision regarding Padme dying in childbirth. He does not want her to die in a similar way. That, his increasing arrogance and his hate for the Jedi Council, all combined, are the reasons and motivations for Anakin to fall to the Dark Side. Which means it was time for Palpatine's revelations. He reveals that he knows of a power to save people from dying, and later that he is a Sith Lord, knows of his wife, and has the knowledge to save Padme. So after Anakin reports Palpatine to Mace Windu, waiting in the Council chambers, he returns and after a moral dillema, kills Mace Windu (then has a shock), and then pledges himself to Palpatine. But that's not the end of it. His arrogance is at maximum level, so he plans to overthrow Palpatine, and plans to rule the galaxy with Padme and the children. Of course it doesn't happen, Obi-Wan comes, they fight, Anakin *suffers*.
This is the summary of what happened to Anakin. This progression is natural, and all that has happened relates to each other. Anakin's fear of loss, mistrust for the Jedi and his arrogance, COMBINED, is what causes Anakin to fall. If any one of them were gone, Anakin would not have fell. If he didn't want to save Padme, he wouldn't fully embrace the Dark Side, and would probably go grey. If Palpatine didn't cause him the mistrust for the Jedi, again Anakin wouldn't embrace the Dark Side. He wouldn't notice the council's corruption and side with the Jedi when the time was right.
Now then, let's examine what has been said:
Palpatine telling Anakin that he doesn't know how to save Padme basically would render Anakin's fall completely pointless. But he was stupid so he didn't care. Is this movie-breaking? It looks like if his motivation to save Padme is destroyed the whole thing crumbles. And he is too stupid not to notice Palpatine lied to him. And yes, him killing the Younglings is too rushed and forced. Maybe the execution isn't as great as it is. But only these. The motivations and actual fall to the Dark Side, I feel are great. The Jedi thing should have been focused on a moral side than a political side though, I agree. And it's after Anakin falls that he starts to do forced things. All it would take would be to edit out Palpatine saying "...if we work together blah blah..." and killing children, and it would be fixed. But does these make the execution poor?
You know KotOR II did the morality/complexity of the Jedi much, much better.