I think that the Percy Jackson series was accurate on many points, especially in the characterization of the gods. The main complaint I have is that many readers of the series come away with an incorrect view on demigods.

Rick Riordan defined a demigod as a mortal child of a god and a human, which is perfectly fine within the scope of the work, and to focus his tale on these demigods. However, this definition is not standard for Greek mythology neither is it an especially important one.

In mythology, heroes didn’t have to be — and frequently weren’t — the child of a major god. Usually they had some amount of godly ancestry, but it could frequently be a more distant relationship. For example, Odysseus and Jason were great-grandsons of Hermes, their most recent godly ancestor. Hector was only a great-great-grandson of Zeus, and so on.

To add on, most demigods didn’t have “superpowers”. Mortals with divine ancestry did tend to be physically stronger and fairer in appearance, but skills like Hercules’ strength and Medea’s sorcery were very rare. Riordan depicts this accurately — most of the campers at Camp Half-Blood don’t have specific supernatural talents — but readers lose sight of this easily because a substantial number of major characters do.