Replacing the infinite switch fixed Problem #1. It was easy enough to do once I had the right switch but would have been even easier if there had been a printed diagram of the terminals on the new switch. If I really needed to I could have taken a minute to draw my own though and label the wires as I removed them from the old switch.
Problem #2 was solved by simply blasting the switch with an aerosol electrical contact cleaner available at any hardware store.