1. There is a tunnel system called the "utilidor" that spans the entire park so that employees and cast members can travel about unnoticed.
Contrary to popular belief, however, it isn't actually underground. It was built at ground level and the Kingdom was built on top of that. In fact, the soil excavated to build the Seven Seas Lagoon was used to lift the level of the Magic Kingdom.
2. In the "Be Our Guest" restaurant, there's a secret menu item you can request.
Ask for the "grey stuff" (which is referenced in the Beauty and the Beast song "Be Our Guest") and you'll definitely get a special treat.