So, I find many things problematic about Aang's character:-
His reaction when he found about the genocide. So Aang knows that it has been 100 years and he sees nobody at the Southern Air Temple. Yet, he his cheerful. When he finds about Gyatso, he is very angry. But in the next episode, he is again cheerful at the Kyoshi Island. Like, imagine losing your whole culture, your people, all your friends and family, etc. It should have had more impact on Aang than the poison had on Korra. Remember when Appa was taken away. He felt so angry and sad for many episodes. But why didn't he had very strong feelings when he got to know about the genocide.
Aang was not ready to kill Ozai and it is good that he defeated him without killing. But why does no body ever say that how he must have killed so many people before, like in Season 1 finale, the Northern Air Temple seige, how he killed an insect in the desert, etc.
Why is killing Ozai bad? Does he not want to kill because it would cause him pain? But then keeping him alive in jail would cause him more pain?
When did the show said that Ozai had to be killed in order to be defeated? Why Aang had to face him alone? He could have taken help. There is no rule. And even if Ozai's bending has been taken away, doesn't he still have political power? What about his army? What about the citizens who had been brainwashed?
Again in season 3 start, Aang is extremely disappointed and all. But in the next episode he is again cheerful. How can his feelings can just go away such fast?
Doesn't Aang get things done too easily? Like in season 1, the ocean spirit helps him become Koizilla and they win. In season 2, when Aang is killed, Katara brought him back. In season 3, a lion turtle randomly shows up just when he wants. And in the fight between Aang and Ozai, he accidentally unlocks his chakra and goes into the Avatar state which is too powerful for Ozai.