Character mistake: When Jet tells Katara and Aang to waterbend the water from underground in the geysers, Katara states that she has never waterbent on water she couldn't see before. However, six episodes prior to this, in 'The Warriors of Kyoshi', she waterbends the water out from Aang's lungs to save his life.
Suggested correction: That was a moment of desperation on her part, and she probably doesn't think of it/think she can do it again without the same desperate impetus, Furthermore, the water in Aang was only a small amount and very close anyway.
Regardless of if she did it in desperation or not, she did use bending on water she didn't see. The mistake isn't suggesting anything about Katara's ability to waterbend unseen water, the mistake is only in regards to the statement Katara made about never using bending on water she can't see. And for Katara to forget the one time she used bending on water she didn't see would qualify as a character mistake as well. Now if she made the statement "I don't think I can do this" or "I've never used bending on underground water", etc, that would not be a character mistake.
Continuity mistake: When Zuko and Iroh are walking towards Azula's ship, the gold flame insignia on the imperial firebenders' uniforms switches directions between shots.
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?
The Tales of Ba Sing Se - S2-E15
Audio problem: After Toph deals with the bullies, she explains that she does not care what she looks like. The lip syncing is off. (00:04:09)
Audio problem: When the fire nation guard is hitting the alarm bell, the last hit before the next shot is not heard. (00:09:50)
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.
The Ember Island Players - S3-E17
Other mistake: When they are watching the recap play Toph says she can't see it because they are on a balcony, but when her character comes on she describes him as buff.
