The worst place is if they get into an oven - it takes forever to burn the urine smell out of the insulation. YUCK. Something to be said for old cast iron stoves up on legs!
Turns out that wasn't actually the problem - even after I cleaned that out and repaired the one chewed wire, the machine still wouldn't run - turned out to be the lid switch, contacts were dirty and the linkage a little loose. Whew, don't need to be paying for a new washer right now.