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.
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)
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)
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.
Audio problem: When Toph feels and hears the tank train coming for the first time, she says, "There's something coming toward us," as she runs out of her tent. She turns her head away from the camera after she says "There's," but for the time her mouth is visible, it is not moving as she is speaking. (00:03:11)
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)
The Desert - S2-E11
Other mistake: At the start, when Toph says, "I can hardly feel any vibrations out here," Aang moves his head, and it briefly duplicates. Right after that, Aang seems to shift into another position without any animation, most noticeable with his head and face. (00:01:56)
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)
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)
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.