Promoted Fanboy: Viktoria "Vika" Ridzel, also known as Viria, is renowned for her fanart of PJO characters to the point where they were considered Better Than Canon, with even Rick Riordan giving her his full support. In 2017, Ridzel was commissioned by Riordan to provide official character art for his website.
Write Who You Know: As part of Written for My Kids, Riordan specifically wrote demigods as being afflicted with ADHD and dyslexia so his son and other similarly affected kids can relate. Specifically the story first originated as something he told his son after said son asked him to make new stories about Greek Gods.
California Doubling: The Lotus Casino scene takes place in Las Vegas of course. But that scene, including exteriors, was filmed in Vancouver.
Dawson Casting: The titular character's sidekicks fall under this even after bumping their age up from the novels. In the book, Annabeth is 13, while in the movie she's 16, and actress Alexandria Daddario was 24 at the time of filming. Similarly, Brandon T. Jackson was 25 also playing a high schooler. This is even more jarring considering that in their most prominent roles coming into the film, they were already playing adults: Daddario in White Collar and Jackson in Tropic Thunder. This sequel was filmed three years later, with Logan Lerman now in his early 20s as well. Justified in Grover's case, as he is said to look older than the others (he has a goatee in the first book already) and is in fact 24, although since satyrs age half as fast as humans, he is the equivalent of a human 12-year-old.
Disowned Adaptation: Rick Riordan does not like the movie adaptations of his books. Upon being told on Twitter that a teacher was planning to show the Percy Jackson movies to her class, Rick Riordan posted a form letter on his blog that students could give their teachers, telling them the movies were awful and a waste of good classroom time. When he was informed that the Disney+ version of the first movie censored a scene, he stated that it would have been better if they censored the whole movie and it just played two hours of "blank screen." He's also admitted to never watching the finished thing - his disappointment in the script preventing him from doing so.
Doing It for the Art: Uma Thurman actually worked with a snake wrangler to hold and interact with several live snakes. This helped her understand how Medusa would feel with snakes growing out of her head.
Dyeing for Your Art: Alexandria Daddario colours her hair blonde for the second movie, as does Kristin Stokes for the musical. James Hayden Rodriguez (Luke in the Lortel run, the national tour, and the cast album) briefly did this as well, before returning to his former shaved look.
Executive Meddling: According to Riordan himself, none of the people who worked on the movies bothered listening to him (which is easily seen if you read the emails he sent to the exacs that he himself leaked and compare them to the final product). It's one of those cases where the entire movie could count, thus why its not a very faithful adaptation.
Follow the Leader: Sea of Monsters has Kronos as the main antagonist despite him spending the entire book slowly reforming in a sarcophagus. Kronos' "Titan made of lava" appearance is also reminiscent of his appearance in Wrath of the Titans.
Suppressed Mammaries: Alexandra wears layers of shirts to portray a girl in her late teens after her more adult roles in White Collar and True Detective, the latter of which especially had shown her to have grown quite voluptuous.
The actress playing Clarisse also playing Thalia and Katie Gardner, and voicing various musicians in "DOA".
The actor playing Luke also playing Ares, the Minotaur, and Smelly Gabe, making him all of the major antagonists besides Kronos, who doesn't physically appear. This one does double duty, being financially pragmatic and serving the plot. When audiences hear Luke's voice discussing plans for the lightning bolt with Kronos in "The Weirdest Dream (Reprise)", they're likely to go Occam if they recognize him and assume it's just the actor in a different role.
The actress playing Sally also playing Silena Beauregard, Charon, and the Oracle.
The actor playing Chiron also playing Poseidon and Hades.
Actor-Inspired Element: There's a minor one from "Bring On the Monsters", which has Annabeth responds to Percy's assertion that they're "never going to once have it easy" with "feeling stoked". This was put in to honor Kristin Stokes, who had been working with the show for a long time and played Annabeth in the Lortel run, the first national tour, and on the cast recording.
Actor-Shared Background: Two. Chris McCarrell and James Hayden Rodriguez, who played Percy and Luke respectively, share traits with their characters.
Chris McCarrell really does have ADHD and spent a lot of time in his younger years being underestimated for it before he became a rock star in his field, mirroring Percy's zero to hero arc.
James Hayden Rodriguez had a father who wasn't in the picture much, and struggled heavily with resentment and anger because of it.
Cut Song: "The Little Minotaur", "Pick A Side", and "Take the Weight" from the musical. "In the Same Boat" was partially cannibalized into "Drive".
Dawson Casting: The musical also indulges in this, despite keeping the characters' original ages. Semi-justified given that there's an inherently higher demand on suspension of disbelief in theater productions than in film, and what you can do with special effects, harnesses, and stunt doubles in a movie is often a liability lawsuit waiting to happen in a live production, particularly when underage actors are involved.
Irony as She Is Cast: A minor one from the cast recording of the musical. Chris McCarrell, who played Percy, admitted in an interview that he hates the ocean.