These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
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?
Azula's apparent Heel-Face 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: Fire Lord Ozai was already this, but he takes it to a whole new level here with his treatment of his family.
Fan-Disliked Explanation: 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." Whether this twist is the true and final explanation remains to be seen.
It turns out that the twist is not true and that Ozai really is Zuko's father after all...but the reason why it's untrue, along with what actually happened to Ursa (or rather, what she did to make herself "disappear"), has become an entirely new Fan-Disliked Explanation. To wit, Ursa wrote that Zuko was not Ozai's son in a deliberate attempt to 1) see if Ozai is reading her letters (he obviously was) and 2) Piss him off if he was (which he very much was). The problem is that Ozai, being Ozai, was more pissed that she dared play an obvious lie that for the rest of his life, Ozai would treat Zuko like he wasn't his son as punishment to Ursa. Basically a royal Nice Job Breaking It, Hero moment for Ursa.
Jerkass Woobie: Azula naturally continues to be this, with her pain and insanity even worse than before.
Also, Koh the Face Stealer, who doesn't even appear here, becomes one due to his revealed backstory and Freudian Excuse.
Ron the Death Eater: Admittedly, while what Ursa did was terribly tragic, 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: OZAI, which is hyperbole to the extreme.
Basically the whole trilogy is this, especially Ursa's story.
It gets worse when said story has a Bittersweet Ending, with most of Azula's issues (and sanity) still unresolved, and the future status of how Zuko, Ursa, Ikem, and Kiyi's familial situation will organize themselves is still very up in the air.
Azula's final scene in the trilogy, in which she confronts her amnesiac, different-faced mother, probably takes the cake for the most heartwrenching moment. Just when you thought she couldn't possibly be more of a Jerkass Woobie, she becomes one.
The look on her facewhen she realises Kiyi is her half-sister. This happy, well adjusted little girl who plays dolls and adores Zuko and... there is so much wrong with that situation.
Also, said little girl's trauma at what happens: her new friend (Zuko) suddenly turns scary to her by insisting that her parents are his parent too, her father reveals several shocking truths he's kept to himself for years, Azula attacks in a violent rage and calls her a replacement for her, her mother gets a completely new face and identity....
Zuko's repeated attempts to reach out to Azula, the open envy with which he watches Sokka and Katara, and the look of absolute heartbreak on his face when he decides that he can no longer justify putting those around him in danger for the sake of giving his sister a second chance.
Azula: Zuzu, how could you be so naive?!
Zuko: You're right. I have been naive. [To Sokka and Katara] Take her down.
Then, of course, his last scene with Azula.
Zuko: Come back, please! I can help you! I want to help you!
Azula: Same as always, Zuko...even when you're strong, you're weak.