Maybe a group of Titans who have escaped Tartarus and are trying to create chaos in the world. They oppose the order and justice that Percy, as the son of Themis, represents. They would try to stop him from using his powers to restore balance and would constantly be attacking him and his allies.
Another option could be some power - hungry demigods. They might not like the idea of Percy, as the son of Themis, having the potential to bring real justice to the demigod world. They could try to undermine him at every turn, creating all sorts of obstacles for him in his quests.