Not only can rodents do tons of damage by feasting on the wiring, but they can also lead to maddeningly difficult-to-diagnose problems if there is a wire way out of sight that was chewed on just enough to allow it to short under damp/wet conditions, or when the wire is shaken a certain amount during operations.
I have an acquaintance who spend thousands trying to get a weird problem in her car fixed, until she finally found a mechanic who was willing to put his money where his work was, and stuck through with it until he had replaced enough wiring in the car that the problem cleared up. He also went painstakingly through all of the wires he pulled and was finally able to find a wire that had been chewed just enough that it caused a problem when it got damp and the car was operated at certain speeds, which caused a vibration that made the wire touch the metal frame.