First things first. The anime isn't as good as the manga. Up to episode 25, the anime follows the manga quite closely, but after then it goes it's own route, gets lost and then finds it's way to a satisfactory ending.
Here's where I think it goes wrong:
Making the homunculi failed resurected humans. One of the joys of the manga is the way Hiromu Arakawa has clearly researched the various forms of alchemy that “existed” in the real world, the Xing alchemists missing from the anime being one of the best examples. The manga's homunculi are true artificial creations, and include part of their creator as their ingredients, much as classical homunculi did. While I think the anime gets some good use out of their new origin, it does lead to the worst element of the anime…
Wrath.
Wrath is the Scrappy Doo of FMA.
Interestingly, director Seiji Mizushima was also responsible for another series that went waaay off the rails once it left the manga's story behind – Shaman King. It's almost like they had that show's Lyserg in mind when they created that annoying whiny pile of ressurected flesh.
Despite the clumsy 3/4 of the show, overall it's an enjoyable watch. All the episodes up to 25 are especially good, and the climax makes you forget the terrible lapse of judgment that is Wrath.