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Errors in geography
Street scenes supposedly in Washington, DC show wires for electric trolley buses. There are no such buses in DC.
While Percy and the group are riding in the taxi cab, Percy puts his seat belt on. When the taxi splits in half and Percy is seen hanging onto both sides of the cab, he no longer has his seat belt on.
(at around 1h 18 mins) As Percy is thrown into the air by the cyclops, he is holding the Fleece but while he is in the air he has nothing in his hands. It reappears the next shot when he is on the ground.
When they are fighting the cyclops and Percy has the fleece, he starts running with the fleece in his hand, the cyclops knocks him into the air, and as he's flying through the air the fleece is gone. It reappears in his hand when the shot changes and he's sliding off the table onto the ground.
The inflatable boat leaves a wake behind it when speeding down to the mouth of Charybdis - even though it's actually being propelled by the falling water.
When Annabeth discovers the magical powers of the Golden Fleece on a tablet when she is seen running over to show Grover, you can almost barely see that the tablet has nothing on it.
The camp is attacked by the Colchis bull, which makes a loud bang as it bursts out of a house - yet the giant mechanical beast was totally silent while it crashed into the rear wall, and then tunneled all the way through the entire building.
When Percy and others are being swallowed down to the mouth of Charybdis, in one scene, all three of them are dangling off the side of the inflatable boat. In the next scene, they are all back in the boat and seated upright.
The "Confederate zombie ship" that is supposedly the CSS Birmingham has a rotating radar antenna, an anti-aircraft flak gun (which later appears to be automatic) and WW2 style windows on the command bridge. Even within the fantasy presented by the film, there is no logical reason for this.
Street scenes supposedly in Washington, DC show wires for electric trolley buses. There are no such buses in DC.
In the Washington DC scenes, there are skyscrapers in the background. The Heights of Buildings Act of 1910, limits the height of building, the tallest being 210 feet, not the blue glass building shown in the background.
Polyphemus wears the Golden Fleece, which is said to have the power to heal or cure anything, on his shoulder throughout the film, yet his eyesight is still greatly affected by the injury he sustained from Odysseus, enough so that he mistakes Grover for a female cyclops.
The movie flip-flops on whether cyclopes can pass through the barrier surrounding the camp. Tyson could do so on his own, due to being a son of Poseidon, while the cyclopes who killed Thalia could not. In the original books, as in Greek mythology, all cyclopes were sired by Poseidon, meaning any of them could've entered the camp at any time, according to the reasoning used for Tyson.
The Sea of Monsters is said to be outside of Poseidon's domain, which is why Percy cannot manipulate the water to help them escape from Charybdis. If this were the case, then his other water-based powers, such as his navigational intuition and healing abilities, should not have functioned properly, either.
After Kronos is dispatched and his followers flee, they leave his sarcophagus behind, which Percy and his friends neglect to destroy or take with them on their return to camp. The ending shows that it was simply left on the island, completely intact and unattended.
Percy's narration refers to the four children in the opening as half-bloods. However, one of them, Grover, is actually a satyr, and isn't a child of one of the gods.
Although the daughter of Zeus that appears at the end she pronounces her own name wrong she said it was Talia (pronounced Ta-le-a) when it should be Thalia (pronounced thay-le-a or thal-e-a).