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.
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.
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.
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.
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 and Annabeth are talking by the pool, Annabeth has a red mark on her arm, which she explains was given by the woman who was turned to stone by Medusa. However, in the earlier scene, there is no trace of the mark.
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 normal casino; it is a supernatural entity with its own rules.
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.
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.