After the confrontation with Yon Rha, Zuko tells Katara that her mother would be proud of her choices. Katara wants to express that she's forgiven Zuko, but can't quite bring herself to say it, so she says that her mother would approve of him, and recalls some fond and amusing memories of her mother.
"For the first time in forever, thinking about my mother made me want to laugh instead of want to cry."
When Zuko and Toph talk about Toph's parents disregarding her accomplishments and still thinking of her as a weakling who needs to come home for her own good, Zuko says he knows what it feels like to have to prove yourself, and says Toph doesn't need to prove herself to the Gaang. He also offers Toph a place to live after the war, and Toph gladly accepts, showing a great understanding of Toph and what she wants.
Although Zuko misinterprets it at first, Lu Ten's last letter to him tells him to be himself, to look out for those closest to him, and to live a long and happy life. It's touching to see how much Lu Ten cares for Zuko, telling him to accept who he is in a way that few others did at the time.
Zuko reading Love Amongst the Dragons to Toph. Not only is this a very cute scene, but it's the first time in a long time that anyone has read a story to her.