Aang and Zuko's talk during the fireworks, while everyone else is having a good time Zuko goes and puts poor Aang on the spot with his vow to kill the prince should he ever get out of hand.
Aang severing his link with Roku and crying a Single Tear, signifying that he knows this is what must be done, but still feels conflicted about it. While Roku urges Aang to make harsh decisions, even with regards to his own great-grandson, he's essentially trying to help Aang avoid his mistakes, and it's sad seeing him call out to Aang one last time before he's cut off.
Watching Zuko's slow breakdown is awful, because it goes on for so long. Yes, he made some really dumb mistakes, but he's a teenager who's been put in charge of a nation responsible for world-wide damage, has dealt with multiple assassination attempts, and is afraid he's going to end up like his megalomaniac father. The moment where he slips off a cliff created by Aang is heartbreaking, because for all his insistence that Aang kill him if needed, he looks terrified.