Note: I don't think I'm giving anything important away, but tread carefully just in case.
I was so glad when I found out Rick Riordan was writing this. I had a feeling he would do a spin-off type thing of the Percy Jackson series.
I had three problems with the book that kept it from getting five stars. (If it was an option, I'd give the book 3.75 or something.)
First: I missed my snarky little Percy! Jason, Piper and Leo weren't flat characters, but their narration just wasn't quite as entertaining as Percy's.
Second: I had issues with the story being told in third person. Of course, I understand why Rick Riordan did this, since it's much easier to change perspectives in third person without confusing the reader. However, his writing style didn't quite mesh with third person. He has a habit of addressing the reader with "you" and a lot of his jokes are told in the narrator's thoughts. That's fine, but it doesn't flow in third person. I feel like that works best with first because first is more personal, less formal.
Third: As a reader, I felt that I was launched too quickly into the "weird" stuff--Tia Callida, the "Dirt Woman", things like that. It seemed a little random and stretched. My brain had trouble wrapping around it until Riordan explained it towards the middle of a book. That's a long time to keep a reader confused like that.
Don't get me wrong, I still enjoyed the book. I don't think I'll ever like it quite as much as Percy Jackson, though.