The humming sound coming from an outlet means there is a loose or broken wire causing arcing. Turn off power to that circuit, test for power to make sure it is dead. Open up the outlet and inspect for burned and broken bits. A microwave oven uses alot of power and will burn up an outlet if there are loose connections. Another common destroyer of outlets is portable heaters. RV outlets(called self contained outlets) are pretty cheaply made to begin with. They use a push together connection that holds the wire and will expand and contract causing excessive heat on high powered loads.
Edit: My post was superceded by your discovery. :)