The Northern Air Temple - S1-E17
Plot hole: They specifically say there is a door no-one but an Airbender can open, but then when it is opened, we learn the Mechanist uses it. How did the Mechanist get in?
Other mistake: The Air People were wiped out by the Fire Nation through Suzon's Comet enhancing them, we even have confirmation of this by the dishevelled exposed skeleton of a VIP of them (presumably any Air Nomad who escaped would have given Monk Giatsu honorable burial), but we never see scorch marks on the Air Nomad buildings or the aforementioned skeleton.
Chosen answer: Toph had Katara use it to send a letter to her parents. It never returned.