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.
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.
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.