The Tales of Ba Sing Se - S2-E15
Audio problem: The Tale of Toph and Katara: Right after the scene of Toph and Katara at the Fancy Lady Day Spa, as Toph says, "Well, that wasn't so bad. I'm not... I actually feel girly," her lip movements are out of sync. (00:02:34)
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)
The Tales of Ba Sing Se - S2-E15
Other mistake: The Tale of Aang: After Aang lets all the animals out of the zoo, he takes out his bison whistle and blows on it. As he does so, the way he holds his staff makes it so that it's going right through his head. (00:10:28)
The Tales of Ba Sing Se - S2-E15
Other mistake: The Tale of Sokka: When Sokka delivers his final haiku to the girls, he inadvertently adds an extra syllable to the final line. In the close-up of him counting his fingers, the iris of his left eye is rendered over his hand. (00:14:42)
The Tales of Ba Sing Se - S2-E15
Continuity mistake: The Tale of Zuko: When Jin and Zuko are at the restaurant, some of the items on their table constantly disappear, reappear, and change position depending on the shot. (00:16:30)
Continuity mistake: When Ghashiun orders the sandbenders to ransack Appa's saddle, Appa's eyes are closed. In the next shot, they are open, then go back to closed in the following shot. (00:02:23)
Other mistake: When Aang is reading the letter from The Guru, as Sokka says, "What's a guru? Some kind of poisonous blowfish?" his right eye loses its white colour three times during the shot. (00:18:19)
Other mistake: When the group goes to hug Sokka before he and Aang go to Chameleon Bay, you can briefly see that Toph is incorrectly drawn with arrow tattoos on her hands, like Aang has. This happens very fast, but you can still catch it when watching the episode normally without pausing or slowing it down. (00:20:35)
The Crossroads of Destiny - S2-E20
Continuity mistake: When Aang enters The Avatar State, the arrow on his head is glowing, as it should be. But in one shot showing his backside as he rises into the air, the arrow is not glowing. (00:19:44)
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 Headband - S3-E2
Continuity mistake: When Zuko and Mai are having a picnic, Azula asks Zuko if she can have a word with him. In the next shot, Mai is wearing a black glove on her left hand, which she wasn't wearing in the previous shot. Two shots later, the glove is gone. (00:15:03)
Continuity mistake: Toph mentions the worst thing about being disguised is they don't get the hero worship anymore and she misses the love, to which Sokka grumbles, "Boo-hoo, poor heroes." Then, as Sokka says, "It's just, all you guys can do this awesome bending stuff," the triangular emblem on Aang's red "headband" has vanished, and in the next shot, it reappears. (00:03:35)
Other mistake: When the group is first shown inside the store, Sokka starts running forward. Toph stands behind Sokka, but as Sokka is running away from them, she is layered over him. (00:04:43)
Continuity mistake: After Sokka admits to Piandao that he thought he messed up everything they worked on, when Piandao says, "You messed things up in a very special way," the yellow trim at the front of Piandao's collar is incomplete. The yellow trim is rendered properly when Piandao says, "Your sword must be an extension of yourself." (00:13:55)
Continuity mistake: When Piandao tells Sokka that creativity, versatility, and intelligence define a great swordsman, he holds out Sokka's sheathed sword with its hilt at Piandao's right hand. However, in the next shot facing Sokka, the sword in its scabbard now lies on Piandao's hands the opposite way, with its hilt at Piandao's left hand. The position of Piandao's hands and thumbs changes as well, between shots. (00:17:25)
Audio problem: At the start, when Zuko says, "I feel like a child," his mouth does not move. (00:01:05)
The Western Air Temple - S3-E12
Other mistake: When Sokka and Aang put Toph's feet into the fountain, Aang's hand (the one holding Toph's left leg) is incorrectly drawn with a blue glove on it. The glove is gone in the next shot. (00:15:29)
The Firebending Masters - S3-E13
Other mistake: When Ran and Shaw (the dragons) breathe the colorful fire around Aang and Zuko, and the camera moves down to them, Zuko's scar is on the opposite side of his face, and his sword and Aang's clothing are worn over the opposite shoulders in a mirrored shot. (00:20:01)
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)
Answer: The pirates are from the episodes "The Waterbending Scroll" and "The Waterbending Master" (They're the ones Katara stole the scroll from). The traveling musicians are from "The Cave of Two Lovers. The prisoners of war likely refer to the Kyoshi Warriors, the men of the Southern Water Tribe, and possibly Bumi and the other citizens of Omashu.