There are two recommended services. Kids Nite Out and Fairy Godmothers. if i'm not mistaken, one is primarily older caregivers while the other is more college aged (if that's so, i also think KNO is the younger crowd).
bottom line is, i've never heard anything bad about either, plenty good about both and if you aren't comfortable leaving your child in the room with whomever they send, you don't have to. these businesses wouldn't continue to succeed or be recommended by Disney without a solid record. especially the latter - i can speak from first hand experience that places don't like recommending outside vendors because if it ends badly, it comes back to the person who recommended it.
http://www.kidsniteout.com