they make non-conductive "grease" (I forget exactly what it's called) that's used to waterproof/prevent corrosion of electrical connections in the engine bay... you can get it at any auto parts store.

take the mirror apart and apply liberally to the back of the buttons, it wont damage the electronics (just make sure it's not creating a barrier between the contactsand it's thick enough that it wont seep out on you either...

I have no idea how hard it is to take apart the mirror but I've done this for button rattles on other cars with great success.