Your stating that the outlet trips when shutting off the light or fan? Seems odd but it could put a surge on the neutral causing the outlet to trip. I would replace the outlet and or confirm there is not a short between the neutral and ground. Not sure what the threshold is for a trip but it could be around 1mega ohm.... If your meter does not go to OL (everload or open) then that could be your problem. Is the tooth brush unplugged when taking this reading?