When Chiron in centaur form walks, he looks strange - but it's not because of bad CGI. It's because a horse, like all four-legged animals, walks with a four-beat gait; whereas whoever animated Chiron clearly didn't know this and tried to force the "walk" into a two-beat, unnatural gait.
The substitute teacher, Mrs. Dodds, writes, "I understand a fury in your words But not your words" on the blackboard, when the actual line from Othello 4.2 is, "I understand a fury in your words. But not the words".
In one scene, when Percy is new to the camp, he & Chiron are talking alone by the lake. When the camera is on Chiron, Chiron's arms are folded. But, when the camera switches to Percy, Chiron's arms are suddenly down.
After Percy beheads Medusa, her body is on the ground as Percy is wiping the sword clean. On her arm is the green pearl in plain sight, but when Percy bends down to pick up her head the pearl is covered by her sleeve.
When Percy is in the Demigod infirmary after the fight with the Minotaur, there is a shield seen leaning against the table next to him as he sleeps. He is then woken up by Grover, the camera angle return to Percy sitting up, and the shield is gone.
In the beginning when Poseidon and Zeus are speaking, Zeus states that the bolt must be returned by the summer solstice. With the solstice "fourteen days away" it must be June 7. This establishes the current season: summer. When Annabeth, Grover, and Percy are in the Underworld, they are greeted by Persephone; however according to Greek myths, Persephone remains in the underworld only during winter. However, in the sequel books, Persephone stays in the Underworld during summer in order to avoid the war of the gods above ground. It is therefore possible that Persephone stays in the Underworld during spring/summer. Since, in the movie, Hades is trying to do battle with his brothers, he might have kept her in the Underworld to likewise keep her out of the war. However, one thing to consider is Persephone mentioned that she looks forward to her "alloted time" away from the Underworld, which is the summer. There is no indication Hades kept her down there to protect her.
The ancient Grecian Perseus was the son of Zeus, not Poseidon. However, Percy here isn't supposed to be the Perseus from original mythology; he was given his name in honor of Perseus. It is revealed in the books and deleted scenes from this movie that Percy's mother had named him after the original Perseus because he was the only demigod to have a happy ending (instead of a tragic death) in hopes that Percy would also have a happy ending.
Both Percy and Annabeth are teenagers and in a real Las Vegas casino would not have been allowed to roam unaccompanied in the gaming area without someone over the age of 21. However, Lotus isn't a "real Las Vegas casino," it is an illusion specifically there to detain people, including underage demigods.
When Percy sees the final pearl in the Lotus Casino, on the spinner, it is on slot 33. When Percy picks it up later, it is on slot 15. While the number did change where the pearl was located, Percy was away from the table to rescue Grover and Annabeth. It is highly probable that the dealer collected the pearl and spun again as he would in a "regular casino" to keep up the illusion.
In the scene in Auntie Em's. Where Annabeth first runs into Medusa, she is wearing a turban. According to lore, Medusa has a head full of snakes, rather than hair. In that scene there is a small piece of blonde hair visible peeking out of the right side of the turban. Uma Thurman has blonde hair.
Annabeth is not able to release her arm from the hand grip of the woman turned into stone by Medusa but when Grover cuts off the stoned statue's arm with his sword, Annabeth is able to remove the stoned hand grip by simply shaking it off although it is clear that it was not broken.
During the fight with Medusa, she knocks over a row of statues which fall on Percy, trapping him. As he tries to free himself it is clear that he was not stuck; none of the statues was even touching him.