The Lightning Thief is a good adventure story though the ending feels a little rushed, and the book feels dated. I didn’t notice so much the first time around (or didn’t remember), but the book definitely feels early 2000s (is this the one that references Jesse McCartney? I can't remember).
I'm not sure about the use of crippled at the beginning in regards to Mr Brunner. I didn't think that was an acceptable term to use anymore? Riordan also uses food terms when describing non-white characters. However, he does explicitly state that a few characters are white. I know that in general Rick Riordan tries very hard when it comes to writing diverse characters, so I'm hoping his future books do better.
Also I was reading the Iliad when I was rereading this series, and there are lots of references to mist in there. Half the times it's death but the other half it's gods obscuring things from the mortals.