My first cred has got to go to the set people. It can't be easy turning a small stage into large ships and islands, but Starcatcher did it beautifully. I think my favorite moment was when they used ropes as stairs.
My second cred goes to the writer in turning a 451 page paperback middle grade book into a two and a half hour theater production. The book definitely had plenty of material to work with and the show pretty much stayed true to the story, with the exception of naming Peter "Boy". This is more towards the Disney version when Wendy calls Peter "Boy" in the nursery. In the book, Peter is actually named Peter with no last name, but in the show, he is called Boy until Molly helps him come up with a real name to call him by. A minor change that didn't effect my loving of it. Peter is also the leader of the group in the book always taking command and making himself older than the oldest boy in the orphanage. In the show, they portrayed Peter as more of a loner, a quiet type until he meets Molly. I'm okay with that too.
When I watch any kind of book adaption (TV, Movies, Theater), I always look for the core values of the book. If the basic principle, what makes the book good and likable by it's readers are still there, then I'm generally happy with it. I also base it on my personal feelings toward the story. If the book made me feel like a kid again, then I want the adaptation to make me feel the same way. As for Peter and the Starcatcher, it made me never want to grow up, both book and show.