The Siege of the North (Part 2) - S1-E20
Corrected entry: When Aang is talking to Koh, Koh says that the Avatar tried to kill him in a past life, 800 or 900 years ago. Later on in the show, when Aang is on the Lion Turtle, it is revealed that it was Avatar Kuruk who tried to kill Koh. Kuruk was the Avatar before Kyoshi, who was born 400 years ago, as was revealed in The Warriors of Kyoshi. There is a 400 year gap between those events that doesn't fit together. If Kuruk was 400 years old, it would contradict what is stated in Avatar Day, because there, they said that Kyoshi was the oldest Avatar, at 230 years old.
The Desert - S2-E11
Corrected entry: When Aang enters The Avatar State, he starts to rise very high. But when Katara reaches out to grab Aangs arm, she reaches it, but Aang was supposed to be too high!
The Day of Black Sun (1): The Invasion - S3-E10
Corrected entry: Ming brings Iroh White Jade Tea, though Iroh was poisoned by it in S2-E2: The Cave of Two Lovers.
Correction: Actually, during The Cave of Two Lovers, he said the flower was either the white jade or a poisonous flower that would kill him. He apparently decided against the tea and found some berries, that he thought was safe but ended up not being. The berries are what almost killed him.
The Southern Air Temple - S1-E3
Corrected entry: When Aang goes into The Avatar State because he found Gyatso, statues and paintings of the previous avatars begin to glow all around the world, including the Fire Sage's temple. They act as is this was the first time, but Aang already went into The Avatar State before this point, when he thrown off Zuko's ship in the previous episode.
Correction: The Fire Sages are simply responding with astonishment to an event that is still relatively new to them, something that until very recently had not been happening for over 110 years. First time or tenth, it's still awe-inspiring to them.
The Avatar and the Firelord - S3-E6
Corrected entry: Roku dies at the end of the episode because he is about to be engulfed by a pyroclastic cloud. It is made clear that when the Avatar is in imminent danger, The Avatar State is triggered. So it should have triggered, saving Roku, but that couldn't happen for obvious plot purposes, even though it defies what they said earlier.
Correction: First, The Avatar State is only triggered reflexively as a defense mechanism until the Avatar learns to control The Avatar State. Roku has, at this point, long since mastered The Avatar State and so here it is not triggered. Second, entering The Avatar State does not make the Avatar immortal, it just makes them more powerful and grants them the full awareness of all previous Avatars. Not only is an Avatar in The Avatar State not immortal, if an Avatar dies while in The Avatar State, the Avatar line will end forever. Roku knows this, and he also knows he is doomed, which is why he deliberately does not enter The Avatar State. He is trying to preserve the Avatar line for future generations.
The Boy in the Iceberg - S1-E1
Corrected entry: In the scene where you see the children sliding down Appa's tail, in the close up shot it's leaning on the sticks. From far away it changes to lying on the ground, then close up again, it's back on the sticks.
The Desert - S2-E11
Corrected entry: When Aang enters The Avatar State, his eyes and forehead arrow glow like normal, but the arrows on his hands do not.
Correction: It is canonized in the final episode that, depending on how deeply Aang is tapping the power of The Avatar State, his every tattoo does not always radiate with energy.
Correction: Kuruk was the last full-realized Avatar before Kyoshi. But just like Aang was trapped in stasis for a century where the world had no Avatar, all kinds of things could have happened to delay the next Avatar's arrival. War or illness could have killed off an unrealized Avatar as a child, for instance. There could have been two or three incarnations that never became full-fledged Avatars. Maybe Koh's dates are a little off. He says 800-900 years ago; a hundred years is an awful big range of uncertainty. This is all conjecture, sure, because there just isn't enough information to support these claims. But so is this mistake's claim that it is impossible for Kuruk to have killed Koh since there is no where near enough information to support that either. If it were stated outright in the show that Kyoshi was born the very first autumn after Kuruk's death, then we'd have a mistake for certain. But it isn't, so we don't.