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 Boy in the Iceberg - S1-E1
Continuity mistake: In this episode, Katara remarks that "This ship has haunted my tribe since Gran Gran was a little girl. " However, in the episode "The Puppetmaster" it is revealed the ship wasn't beached there until Gran Gran was in her late teens or early twenties.
New this weekSuggested correction: If Gran Gran was really in her late teens or early twenties during the Southern Water Tribe raids, that can still be considered a "little girl," since she is in her eighties in the show.
Suggested correction: You sure that was the same ship, and what's 5-10 years give or take compared to Gran-Gran's life anyway?
Imprisoned - S1-E6
Continuity mistake: When the gang meets Haru, Katara teleports from behind a log (shoulder still visible) in one shot to greeting Haru several yards in front of the log a split second later. (00:02:50)
New this monthSuggested correction: That's because the second shot is a jump cut. The trio first sees Haru from behind the log, and after Sokka says, "He looks dangerous, so we better approach cautiously," the scene jumps forward in time to Katara greeting Haru further away from the log. Katara simply got closer to Haru, which was not shown.
Continuity mistake: When Azula is asking Zuko whether or not he thinks the avatar may have survived, Zuko goes into a flashback. When he snaps back to real time, Azula has her hands behind her back. When the shot cuts, her hands are instantly by her side.
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)
Continuity mistake: In the shot after Mai says "Saving the jerk who dumped me" you can see the rods which the prison guards used to slow down the mechanism of the gondola are nowhere near the wheel. (00:19:55)
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.
New this weekSuggested correction: She didn't see him (or technically, feel him), but she heard him. The actor playing her character throws the huge prop rock, and it hits the stage floor. Then, he flexes his muscles. Toph heard all this happening from her seat and then said, "I sound like a guy. A really buff guy."