Nathan Fillion, as Hermes, gives Percy a thermos from an Olympian TV show about Hercules, commenting about what a great show it was, and how it was canceled prematurely. Nathan Fillion was one of the main stars of the sci-fi series Firefly (2002), which was canceled after only the first season, even though the series was incredibly well received.
Nathan Fillion (Hermes) remarks how adorable it is that Percy and Annabeth are finishing each other's sentences. In the TV series Castle (2009) (staring Fillion) it's also remarked how the two main characters are always finishing each other's sentences.
Many aspects of the story were greatly changed from the source material, such as the poisoning of Thailia's tree, the bronze bulls attack on camp half blood, and Kronos not actually appearing in the books themselves until the fourth installment, the labyrinth.
Obviously Percy is not the only living offspring of the three main Gods. Among others, the list of Zeus's children include Dionysus, Aries, Aphrodite, Apollo, Hermes and Persephone. Which is kind of funny since it means that the Cyclops Tyson is not only Percy's half brother, he's also Mr. D's cousin!
Through out the movie Mr.D (Stanley Tucci) never gets Percy's (Logan Lerman) name correct. Once he calls Percy, Peter. A possible reference to the movie The Lovely Bones, which was directed by Peter Jackson.
The trivia item below may give away important plot points.
The three demigods who have joined Luke are Silena Beauregard, Ethan Nakamura, and Chris Rodriguez. However, in the books, Silena remained with Camp Half Blood and did not defect to join Luke's gang until the fifth book.