Avatar Day - S2-E5
Continuity mistake: When the village leader switches the wheel of punishment to Community Service, it is on the space next to Boiled in Oil. However, all of the other shots of the wheel have another section in between these two.
Bitter Work - S2-E9
Continuity mistake: When Iroh draws the symbols of the Four Nations in the sand, there is grass on the left side of the Earth symbol in the close ups. In the shots that show all four symbols, the grass is gone. (00:14:25)
Avatar Day - S2-E5
Continuity mistake: When we first see Aang in the stocks, Sokka advises him to use his Airbending to escape and begins "imitating" Aang's kata. During one pose, we see Sokka is wearing the boomerang, or at least the sheath it was in, that he had to leave behind at the beginning of the episode. He wasn't wearing it before, isn't wearing it after, and doesn't actually get it back until the climax. (00:02:09 - 00:06:33)
Continuity mistake: When Katara is trying to heal the wounded earthbender, she gives Sokka the idea to take down The Drill from the inside. Sokka then stops her from saying anything while she is sitting down, and she is wearing her necklace. When she stands up in that same shot, the necklace is gone, like they forgot to animate it. (00:07:35)
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 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)
Chosen answer: When Sozin says "So I wiped out the Air Temples," we are indeed seeing the three mountains of the Eastern Air Temple burning, with the two bridges being gone in this shot (S3-E6). This does conflict a bit with the image we see of the Eastern Air Temple, with the two bridges intact, when Aang and Appa fly to that Air Temple seeking Guru Pathik (S2-E19). This may possibly be considered a mistake, but the fact is that when we are seeing the burning of the Eastern Air Temple it's from the point of view of Zuko, who is merely reading from Sozin's autobiographical account, and envisioning everything he's reading, which in his mind includes the bridges having been destroyed.