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.
Suggested 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."
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.
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?
Suggested 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.
Plot hole: Because Katara lost her mothers necklace, Aang made one for her and she puts it on. But when they reach The Fortunetellers village, Katara is not wearing the necklace, and no one notices, not even Aang.
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)
Suggested 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.