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.
Other mistake: When the gang is in the Hall of Statues of Past Avatars, Katara points out the avatar cycle pattern of statues and Aang zeroes in on Roku's statue. The earthbender avatar statue next to Roku is of an unknown man with a sword, not Kiyoshi. (00:12:50 - 00:13:35)
Other mistake: When Azula attacks The Western Air Temple, there is a close up shot of her when she says that she is about to become an only child. Pay attention to the smoke coming from the airship behind her, especially above her head: it doesn't move. Even if this was remotely possible, it does move when the camera zooms out, making it a mistake nonetheless.Friso94
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)Phixius
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)Friso94
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.Lord Mordo