Is there a common reason why the windshield wipers would not turn off? Perhaps a contact or broken switch?

haha mine won't turn on.
Let's trade!

... a house in Seattle ?

seriously, If you talking about a 4 cly car. the wipers work by switching the ground you could use a test light and start with the switch to be sure the trouble isnt there (maybe one of the wires is grounding there), then try the plug at the motor, last check the motor itself and the fuse panel.

Worst case I'll just add another switch.