I sent off my second iPod to get it repaired. Its battery was running down overnight unless I kept it plugged into the USB recharger. Also it displayed the AC charger icon on the screen unless I was working with the menus. The strange behavior of random click wheel movement without touching it seems to have stopped – or maybe it just dried out. Nevertheless I sent them a movie of that behavior, but I doubt that they’ll even look at it.
Update: The new one (this’ll be number three) is on its way from Hong Kong.