Uncle Iroh comes off as a buffoon as often as he does a wise old mentor. But the buffoonery is in such diametric opposition to a long and storied career in which he was, until Ba Sing Se, an extremely successful general that the simplest explanation is that he does it to distract Zuko from focusing on how awful his lot in life is and to mask that he's surreptitiously setting up lessons for Zuko. If the buffoonery is genuine, then Iroh's buffoonery may border on a trope of a different color... but the line between buffoon and wise man isn't usually that pronounced. In Season 3, he's explicitly shown using Obfuscating Stupidity; any earlier "buffoonery" can be attributed to attempts to look harmless so his psycho little brother Ozai won't try to have him killed and endanger anyone who gets caught in the crossfire.
There's a subset that was so moved by her Villainous Breakdown that they decided she wasn't a sociopath. She's shown in canon to be cold and manipulative, using fear as a weapon and then calling it friendship; in stark contrast, part of the fandom seems to have decided that she's lost, scared, and just wanted Mommy to love her — as opposed to, you know, being a murderous bastard caught in deep psychosis. A few think it's both — one led to the other. If Azula was so lost and scared as a child, then becoming so powerful, manipulative, sociopathic bitch would (in her mind) seem like an ideal solution to erasing all the pain.
The real potential head case of the Avatar universe is Ozai. Viewing Zuko as a reflection of who he was as a child, a sensitive Momma's Boy who fails at every attempt to please Daddy, and his bigbrotherwhom everyone loves doesn't make things any easier. No Azula represents his idealized self,in THAT way along with her perfection as a Bender, intelligence and natural born leadership skills. He indulged Azula as he wished he could have been indulged as a child. Perhaps he genuinely loved Azula but spoiled her rotten for the reasons above, he tried to love Zuko but he couldn't due to his own self loathing.
It's also known that Ozai inherited the Fire Nation well into the Hundred Year War; there's also no mention of military accomplishments on his part, at least on par with his brother's. It's possible that his overzealous pursuit of glory for himself and the Fire Nation stems from an Omashu-sized chip on his shoulder. The way Zuko goes to him for advice during the sequel comic, The Promise, also implies that there was more, and more complex, issues on his solid-gold plate than figuring out which people and lands to subjugate. Any chance for sympathy probably ends when he decides to raze the Earth Kingdom to the ground, though.
It's possible Ozai saw himself in Zuko and was being hard on him to instill the strength in his son that being second-best instilled in him. Forgetting what happened to his own father as a result... Or even expecting it and wanting his son to kill him later on. That way he could be truly proud at the very least. It's possible than the main reason Ozai was angry in the Day of Black Sun was that Zuko was trying to join the Avatar and end the war instead of trying to do a better job leading the effort. He'd even posit that Ozai probably would've been far more satisfied if Zuko killed him right there. He still saw Zuko, even in defiance, as a coward.
Many viewers saw Zuko as a very troubled and sympathetic guy who legitimately struggles with various aspects of his life and himself, and sometimes has periods of whining (but understandably so), which thus makes his maturing a truly amazing story to watch. A number of others saw him as a pathetic, loser teen with serious anger problems and a general fuck-up who constantly causes unnecessary trouble for everyone, including himself.
About half the fandom considers Sokka to be a sensitive genius with occasional moments of idiocy and assholery. The other half considers him to be just the reverse.
Was Admiral Zhao's refusal to let Zuko try to rescue him from a vengeful Kaiju-class Ocean Spirit one last act of arrogant contempt for the boy, or a rare act of wisdom and honor in not letting the stupid kid get himself drowned too?
Is Aang the kind, childlike Air Nomad that everyone (including he himself) sees him as? Or is he a selfish, power hungry —or Naive— child who cares more about his own wants than the happiness of his family and friends or the needs of the world, even if it means destroying the balance he's supposed to maintain?
Asking why Iroh never bothered to overthrow his murderous usurper of a brother and saddled his emotionally damaged teenage nephew with the job of running the Fire Nation will start arguments, although him not overthrowing Ozai is at least given an (admittedly short) explanation in the finale.
Iroh's retirement to his tea shop: old man stepping aside to give the younger generation a chance to build a new world order or covert political hostage to the Earth Kingdom in order to secure a peace treaty?
Was Ursa a perfect mother, a humanly flawed woman, or a bitch who blatantly played favorites and ruined her daughter forever? The show gives us the first characterization — but it comes from Zuko's personal memories, making it possible that Zuko is simply idealizing her out of his love for her. Ozai and Azula would probably think of her as the second and third characterizations respectively.
This trope was deliberately cultivated for most members of the Fire Nation Royal Family. The writers were afraid that anything they came up with would be too dark even for this show. They intentionally left details vague so the viewers could make their own ideas.
Zutara shippers frequently portray Mai as a cruel, insanely jealous bitch, though she's just as easily a confused and possibly depressed teenager just as messed up as the rest of the Fire Nation characters whose character development, while less overtly stated than Zuko's, nevertheless paralleled his enough to give her a Heel Face Turn near the end of the series.
Sozin/Suesan - Conquering the world in order to share the country's economic influences; or a boy named Sue who becomes a Monarch of Darkness and seeks revenge on the world for cursing him with a girl's name.
Azulon - For a character that has had only a few minutes of screen time and a couple lines, there is so much debate about him and the ambiguous scenario involving him. Did he ask Ozai to sacrifice his son for a slight against his eldest? Was it a Secret Test of Character? Was Azulon speaking figuratively*
Ozai would lose a son because Iroh would adopt Zuko as his son and heir completely by-passing Ozai's chance to the throne
? Did he even give that as an order or did Azula make it all up (for any various reasons) and Ozai went with it?
Jeong Jeong - Antagonistically dour, but correct in that Aang needed the emotional maturity from learning Waterbending and Earthbending before attempting to learn Firebending? Or just a scarred, bitter, self-loathing (and possibly somewhat crazy) old man who simply didn't want to pass on his knowledge in a bending form he considered inherently evil? Plus, his efforts at teaching; fair but strict for Aang's own good, only turning out badly because of Aang's natural flightiness? Or half-assed due to resentment of being bullied into teaching Aang against his will and so all but deliberately setting Aang up for burning Katara?
Avatar Kyoshi's willingness to kill an enemy (when she could find not find any other solution to deal with Chin the Conqueror) has somehow turned into the fanon interpretation that Kyoshi is a killer who constantly revels in bloodshed. This is mostly prevalent when she is compared to other Avatars.
Then there's the fact that Kyoshi is implied to have basically let Chin the Conqueror run rampant over the Earth Kingdom until he had the nerve to approach the area she claimed as her own territory, whereupon she simply broke the peninsula off and turned it into an island. So, Kyoshi the apathetic and only concerned with her own people Avatar?
Yu Dao colony from the Promise Trilogy sequel comic: beacon of multiculturalism and victim of backwards thinkers who don't appreciate its glories, or inherently racist community whose famed wealth is built on making weapons for the Fire Nation's war effort?
Another interpretation of Mako is that Mako/Money is his OTP, the idea that he's a gold-digger. Or at least a young man who goes by practicality. His (paraphrased) statement "I like Korra, but it makes more sense to be with Asami," seems to indicate that he didn't really go with his heart, just with what would be more likely to get him and Bolin further off the streets and Asami was beautiful and kind to boot. It would explain why he threatened to end Korra's friendship for questioning Mr. Sato's integrity. He had come to view the Satos as his new family who would help him out financially, so he kept them close. Korra coming by and calling out Mr. Sato drove a pick through Mako's heart and he stood up for the one wealthy man who ever showed him an ounce of kindness, in denial of the possibility that someone wealthy must automatically be evil, because he had finally torn down that assumption he likely held all these years... Only for it to be proven correct in the one example where he let his guard down.
This may sound bad for any ship involving Mako, but the fact that Mako grew to care about Korra enough that she need not be the Avatar (a person of serious status) to love her indicates that he cares far more about her as a person than anything else... Although, if she isn't the Avatar, she'd still be a former Avatar and one of the few remaining airbenders, the idea that the Order of the White Lotus would cut off all funding and support is a dubious assumption, so if one wants to get really cynical, it could be assumed that he'd rather stand by the girl he likes who could still have high status and financial support, than the one who's father's company just experienced a serious blow.
The fact that it was never entirely clear whether or not Amon was sincere about his crusade against bending despite being one himself or was just taking advantage of anti-bender sentiments to gain power or upstage his Abusive Father makes it very difficult to determine what category of villain he falls under. Whether or not he counts as an Anti-Villain-considering his tragic backstory the real one that is-is up for debate. In the former interpretation, what type of Anti-Villain Amon is- Type III if one thinks Tarrlok was right about him being sincere in his belief that bending was the root of all evil, or simply type II if one doesn't-is also contested.
Tenzin and Lin Beifong: The last light for good government in Republic City, or well-meaning incompetents that only achieved their high rank through nepotism? For all Tenzin's talk about not escalating the conflict between benders and non-benders, he never offers any policy alternatives, and never gets so much as a single vote in favor of his position. Lin is a badass when it comes to combat situations, but as police chief she presided over a city rife with organized crime, let a violent revolutionary movement gestate under her watch, botched the defense of the arena, fell for the Cabbage Corp fake-out, and resigned her post despite knowing full well that she would be replaced by Tarrlok's anti non-bender candidate.
The Park Protestor: Contrarian attention-whore, as Nick's website claims, or an earnest political activist standing up to the pro-bending establishment? Although for all he harps on Korra for benders like her using her power to oppress people like him, he still wholeheartedly supports the Equalists even after they indiscriminately bombard Republic City with their superior martial power... at least until Amon reveals himself as a waterbender. Not to mention that for all his talk about an oppressive establishment keeping down the non-bender, he's allowed to freely agitate for the Equalists in a public park with police protection.
Hiroshi Sato: is his anti-bender attitude simple racism brought about his wife's murder, or is it a way to excuse unfashionable classism? He alone in the show comments negatively about Asami dating outside her social class, calling Mako a "street rat" and expressing his disgust at seeing the two of them together. He's also happy to trumpet in the finale that everyone will finally be equal after Amon's revolution... a revolution that consists only of purging society of benders with no other reforms, and a never-ending world war that will keep Sato's factories busily churning out weapons for the new Equalist government.
A minor case-Pema. Ever since episode six, there's been debate about her actions in the Love Triangle between her, Tenzin, and Lin. On one side, fans are furious at her for breaking up Linzin and have described her as a "homewrecking whore". Pema fans have responded by saying that isn't not fair to judge Pema because we don't have all the details and that Lin and Tenzin's relationship was already going downhill.
Some Tahno fans wonder how much of his taunting was him being a Jerkass and how much was just, well, taunting opponents before a sports competition.
Is the Republic City council corrupt and biased or are they just in extreme stress from the Equalist Revolt and bending crimes?
About all the above? You'll never know because Mike and Bryan won't tell you! MWAHAAAAAAAAAAAAA!!!!!!!!!!!!!!!!!!!!!!!!!!!!