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.