In it, you get some interesting bastardization of Greek mythology, and a moderately lack-luster teenage thriller. Abby was bothered by the mythological inconsistencies (see above link) and wrote up a nice piece on that. So as a companion piece, I thought I might talk about the logical inconsistencies. So, read hers first, if only for the quote at the end (but be warned, it has a spoiler or two).
So, here are my issues:
The identity of the mysterious lightning thief was completely telegraphed. It's like his/her only job in the movie is to set up for the reveal. Some of the mechanisms behind the theft were left vague, but the identity was a no-brainer.
Villains of Greek mythology show up: the Hydra, Medusa, to be defeated by our heroes. Trouble is, they know about their strengths and weaknesses--they know them because these creatures were killed in the Greek myths. How could you possibly know that Medusa's decapitated head would turn people to stone if she was still alive?
Quite a few innocent bystanders get killed, including someone who was annoying but still managed to help protect Percy for many years--and his death was the post-credit "joke". This would bug me less if it weren't a children's movie!
What's with the antiquated clothing? You're telling me that the Greek gods moved Mt. Olympus so that it is accessible via a magic elevator in the Empire State Building, but they still walk around in togas and sandals? I would love to see some contemporary fashion with their traditional motifs threaded in. This would be in keeping with the logic of the film--after all, Hades was dressed like a rock star. Why not put Zeus in a sharp suit or some such?
And my biggest point, and I think this applies to the first two Harry Potter films as well (same director as Percy Jackson): over-acting is not necessary in fantasy films.