Factual error: When Luke is playing video games in the camp he is using a Playstation controller, however when he pauses the game it shows a message telling him to push the 'B' button. 'B' buttons appear on Xbox games consoles rather than Playstations.
Plot hole: In Aunty Em's Emporium, when Medusa turns the older woman to stone, she has hold of Annabeth's wrist and Annabeth cannot free herself. Grover comes along later, as Percy is keeping Medusa busy, and breaks the arm of the statue that is holding Annabeth (near the elbow). Annabeth is able to easily pry the statue's severed arm's grip from her wrist, even though the fingers and thumb weren't broken at all, meaning she could have easily freed herself at any time.
Continuity mistake: When the bus passes Poseidon and he disappears, the people walking near him also disappear. There is an Asian couple walking from left to right across the shot that should have been still there after Poseidon is gone. Sloppy SFX that sort of spoils the effect of a god being able to vanish.
Continuity mistake: There are several scenes where Percy is shown wearing a watch, but it seems to disappear in the next shot or two (most noticable in the Parthenon scene).
Continuity mistake: Sally and Grover are taking Percy to Camp Halfblood; Sally has her head turned to the right, speaking to Percy. Grover, in the back seat, is looking front as he yells for her to watch out. Sally looks forward, and with a surprised look, swerves left to avoid whatever it is she sees. Then the cow, thrown by the minotaur, comes in from behind, above and to the right and lands in front of the car, a direction in which neither Sally or Grover were looking.
Plot hole: Luke states that the reason for hiding Zeus' lightning bolt in Percy's shield is so that he can get the bolt to Hades, and thus start a war that will wipe out the Gods of Olympus. However, this simply cannot work. The whole plot of the movie rests on Percy accidentally dropping the shield, which Percy did innocently and not by any kind of design or planning. Had he not dropped the shield, Percy and the others would have been taken by the souls, Hades would never have discovered the lightning bolt, and the plot of the movie unravels from there.