Percy and Annabeth's ages
There were many things wrong about the appearances of Percy and Annabeth in the movies. One being their age. While Annabeth and Percy in "The Lighting Thief" are described to be about 12-years-old, in the movie, they looked like they were 17 instead of 12. It disappointed many fans how inaccurate the movie was, not only in the terms of appearance but also the story itself.
Percy's claiming is an important part in the story. It is what marks him as a son of Poseidon and gets him involved in the feud between Poseidon and Zeus in the matter of Zeus' missing lightning bolt. This important part was missing in the movie completely.
In the matter of their adventures, the movie was horribly inaccurate, matching only a few things in the book. An example of the inaccuracy the movies showed is the monsters Percy and Annabeth fought in the movie. In the books, they fight the furies on the bus, the Minotaur at half-blood hill, the Chimera and the Echidna in St. Louis, Medusa and Procrustes at the waterbed shop. In the movies, they fight Alecto the Fury (not all three of them like in the book), the Minotaur at the Camp Half-Blood entrance, Hydra at the Nashville Parthenon (which never happens in the book) and three hellhounds. This clearly shows the story line was tampered with and was not at all satisfying to watch for many fans.
In the "Lightning Thief" book, Percy Jackson does not have a shield. Yet, in the movie, Luke Castellan is shown to have given Percy a shield that he later discovers to have secretly held Zeus' master bolt. This isn't right at all, not only because of Percy having a shield but also because of the shield holding the bolt. In the book, the bolt is secretly hidden in the backpack that the war god, Ares, gives Percy, Annabeth and Grover.
Ares does not fight with Percy
Ares is another antagonist, apart from Luke, who fights with Percy at the near end of the first book.He pretends to help them by giving them a backpack and a few other essentials and tells them to go to Los Angeles using the truck of animal smugglers. But in the end, it is revealed that he didn't have good intentions at all. He wanted to use Percy as a way to start a war. In the movie, Ares never appears to them personally and is only seen at the Olympus meeting at the end.
Persephone is never there in the underworld as per the book because, due to it being summer, she is with her mother, Demeter. Persephone is shown in the movie as a hostage of Hades. And she hits Hades with lightning from the master bolt.
Luke's betrayal is revealed at the end of the book in Camp Half-Blood. He then sets a poisonous scorpion on Percy, who nearly dies because of its deadly bite. In the movie, the betrayal is revealed at the very top of the Empire State building where they fight with Percy using his water powers.
Grover remaining in the UnderworldGiphy
Grover, in the movie, is shown to have stayed in the Underworld along with Hades and Persephone before being released by the god of thunder, Zeus. Sally is left in the Underworld until Hades releases her at the end of the book.
Luke getting thrown into the seaGiphy
Luke is thrown into the sea by Percy whereas, in the book, he simply sets a scorpion on him and leaves to finish his true plans of joining Kronos.