Kotaku has already put Kinect through its paces, testing its voice and face recognition capabilities and how well it performs under imperfect lighting conditions. We haven't tested it naked (as far as I know...) but other people have.
IGN UK went there, asking "Can you play Kinect naked?" Yes, you can and it won't detect your "todger flapping around in the wind" according to their bare-ass scientific study. There's video of nude Kinect play in action, confirming that the Xbox 360 camera has no issue detecting pasty game journalist flesh.
The other naked Kinect concern in question: "How do I delete the naked pictures taken while playing Dance Central?" We'd suppose this applies to naked pictures taken while playing any Kinect game with picture taking features, but this one was asked on the Dance Central forums.
"I was trying out the Kinect Dance Central game and I was getting hot so I took off my [clothes] ," writes one Kinect user. "I had no idea that the game was going to take A BUNCH OF PICTURES OF ME WHILE DANCING WITH NO CLOTHES ON!!! I can go back and look at these pictures but HOW DO I DELETE THEM?!!! HELP!!!!"
Look here, Kinect nudists:
My Xbox > System Settings > Memory > Hard Drive > Games > Dance Central
Any other questions?
Kinect: Your Questions Answered [IGN UK]