After Yu Dao blew up in his face, Aang changed. He's willing to compromise on his goals to achieve partial victories. He's become far more practical in his solutions to problems, like punting Yu Dao's reformation to an international conference and advising Zuko to burn a letter that could undermine his claim to the throne, rather than relying on good intentions, friendship, and lucky breaks. He's also being more political in how he treats Zuko, recognizing that his friend is also a somewhat shaky ally who needs propping up after an ambiguously suicidal fall.
Ursa is probably the biggest example: is she a sympathetic and loving mother who was broken by all the pain in her life, or a weak, cowardly, selfish woman who cared more for herself and her old boyfriend than for her own children? Ursa even derides herself for her choice.
Ozai, again. Was he always a heartless, power-hungry Evil Prince and abusive parent and husband or, just like Ursa, was he a victim of his father's eugenic schemes? In some point, did he really try to be a good father and husband?
Exactly what his relationship with Azula is, does he legitimately believe she would be a better Fire Lord then Zuko or was his telling Azula about the letter, something he knew was fake, just prove that she is just another tool for revenge he is trying to use against Zuko and mainly Ursa. Or given Azula's mental state, was it all just a ploy to gain back the throne.
The true reason behind Ozai and Ursa's Arranged Marriage. Was it, as Azulon proclaims, due to the Fire Sages' advice to breed a better, more powerful royal heir with blood of Avatar Roku and the Fire Nation Royal Family or, in reality, was it a calculated political strategy to avoid the rise of a potential threat to the Fire Nation Royal Family's position and power from Roku's lineage, merging the two bloodlines?
Azula's apparent HeelFace Turn is this in-story, as Aang and Katara are willing to believe it, but Sokka isn't and thinks she just slipped up in her craziness and will still be a threat when she next turns up.
Does Zuko completely forgive Ursa for wiping her memories of him at the end? Or is he being a Stepford Smiler and just trying to be a good son to her?
The question of to what extent Iroh knew about or was involved in Fire Lord Azulon's eugenic scheme to create the perfect Fire Nation heir and how much he knew about Ursa's disappearance.
Just like its predecessor, exactly how canon these books are is a debated topic in the fandom; some fans even feel these books almost as a fanfiction, and bringing it up risks starting a fan war.
Complete Monster: FireLordOzai forced Ursa into marrying him, and tried to kill her old lover out of spite. He obtained the throne when he manipulated Ursa into murdering his father to usurp the throne from his grieving older brother Iroh. He then thanked her with banishment from the Fire Nation and threatened to hunt them down and kill the children if she took them with her. He abused his son Zuko out of spite when Ursa claimed that Zuko was not his son even though he knew it was a lie. He doesn't regret any of those moments and feels no remorse for the consequences.
Many dislike the twist that Zuko isn't Ozai's son, mainly because many fans feel it renders pointless a lot of Zuko's character development from the animated series and undermines its original aesop: "You are not your bloodline, your family does not define who you have to be."
Eventually it's revealed that this first twist was a lie and Ozai really is Zuko's father after all, but the reason why it's untrue, along with what actually happened to Ursa, has become an entirely new Fan-Disliked Explanation: Ursa wrote that Zuko was not Ozai's son in a deliberate attempt to 1) see if Ozai was reading her letters (which worked) and 2) piss him off if he was (which very much worked). But Ozai, being Ozai, was more pissed that she dared play an obvious lie that he would punish Ursa by treating Zuko like he wasn't his son for the rest of his life.Nice Job Breaking It, Hero!.
It's not uncommon to find fans who were disappointed with the explanation of how Ursa disappeared.
Some fans were unhappy with the Mother of Faces being Koh's mother as well as the face that he steals faces to spite her. Many felt that this made Koh, an Ensemble Darkhorse, out to be a petty mama's boy and ruined his wise, ancient, powerful demeanor.
Ron the Death Eater: Admittedly, while what Ursa did was terribly tragic and there isn't really any excusing it; even Ursa herself agrees with this. However, some fans take it too far and actually claim she's a worse, more awful parent than Ozai, which is hyperbole to the extreme.