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.
Alternative Character Interpretation: In their final conversation, Aang is "handling" Zuko. He takes an ill and possibly suicidal young man, transport him to the tea shop that hosts the few good memories in his troubled life, lets him see his beloved uncle and sip said uncle's tea, and flatters Zuko with praise about how Zuko was totally in the right about what they'd been fighting over. Aang's statements, however, concede nothing substantial to Zuko. The Fire Nation's single desire was to retain its colonies, and Aang flatly states that no such thing will happen, and that instead the issue will be handed off to a multiparty summit. Whatever the future outcome, Aang walks away from the meeting with three victories to Zuko's zero: he avoids a war, he gets Zuko to implicitly forsake any future claim to sole sovereignty over the colonies, and, more importantly, he gets Zuko back onto his side as a friend. Zuko could arguably claim to have secured the continued residence of the colonists in their homes, but their way of life is going to change with the Fire Nation no longer in charge.
Was Suki's concern over Zuko because of a Bodyguard Crush? Or because of concern for a (platonic) friend she grew close with during their travels in the Gaang?
Broken Base: Just exactly how canon the 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. (Though not nearly on the same scale as the ship wars...)
As of the third trilogy Fan Hate has died down and the comics have become more accepted into canon. Still there is discourse on whether they are a good addition or not. With the end of The Legend of Korra, excitement for the comics has risen as they have become the sole source of continuity for the Franchise, with many fans expressing a desire to see a Korra comic.
The entire Katara/Aang romance is this. Is it cute or downright annoying with the non-stop "sweetie" pet names and oogieness?
Creator's Pet: Gene Yang has described Sneers as his favorite Freedom Fighter, which is why he brought him back for the trilogy. Yang also, incidentally, paired Sneers with a hot girlfriend (Kori) and had multiple characters lampshade how awesome Sneers was for landing a girlfriend seemingly out of his league.
Designated Villain: Zuko is this in-universe to many of the Earth Kingdom people and the Freedom Fighters, and even some of the Gaang like Sokka and Toph. Yes, he's being an idiot, but everyone's treating him like he's already as bad a dictator as his father. Justified considering that they just wrapped up a century-long world war where the Fire Lord was the face of their enemy.
The Scrappy: Kori gets this from fans for her insistance on solving her problems with violence and assassination attempts on Zuko's life. That and the fact that she's a Karma Houdini. She tried to kill the freaking Fire Lord and yet she's free to organize a resistance in the colony.
Some Anvils Need to Be Dropped: Aang's initial rejection of the Air Nomad fan club and eventual acceptance and decision to educate them and set them on a better path as a commentary on cultural appropriation. Cultural appropriation can be deeply insulting, but the possibility of good intentions needs to be considered.
Tastes Like Diabetes: Aang calling Katara "sweetie" in several panels. Ick. This is even lampshaded by Sokka, who calls it "Oogie".
Zuko, when will you learn? You ask someone like Ozai for advice on how to rule a kingdom? Why not ask your loyal and not psychotic uncle instead? Answer: Because for all of his hard-earned intelligence and maturity, Zuko "...is still a stubborn boy." Good thing Iroh's fully aware of this.
Yes Kori, the best way to solve your problems is to assassinate the Fire Lord. Because it's not like assassination of the Fire Lord will cause a civil war, leaving the Earth King free to claim the land, right?