Most of what Zatanna thinks of Percy at this time is second-hand influence from Annabeth, whom she has a lot of trust and respect for because of the Eva connection. This means Percy has most of her trust and respect, too, even though she's pretty certain Annabeth is the smarter of the two. (She also doesn't really mind that Annabeth told Percy, although this might give her more of an incentive to finally come fully clean with Robin. Because guilt.)

That said, from watching their popcorn-worthy interactions together, and talking to both Annabeth and Percy himself, she thinks of him as a very sweet, if somewhat dorky person, who seems to have either horrible taste in music or somebody with horrible taste in music out to get him. She's interested in the fact that he can control water and talk to turtles, and would love to have a long conversation with him about that one day when he's not aura-ed out.