I try not to deify Aang as a writer, but the society in which he lives would deify him the same way ours deifies figures of import. Martin Luthor King, Jr. was actually a serial adulterer, for example, but you try to say anything bad about the King whatsoever, you'll get looks of disbelief because we've been trained to look on him pretty much as though he were holy. Perhaps he was, but he was also human and that came with human failings.
Regardless of what kind of person Aang actually was, he is known as the Avatar that ended the Hundred Years War, had heavy influence over the unification of the 3 remaining nations after years of segregation, build and helped govern a city that is the first of it's kind, and performed numerous other services in his lifetime. There is no evidence of any other avatar being close to this influential in the betterment of the world. I don't even know of any real life historical figure that came close to similar achievements, so I don't even have anything to compare it to. Aang would be basically Jesus among men (And since he is the avatar, that's not even an exaggeration. He IS their spiritual savior taken in the form of a man). But as a person, he'd have human failings as he did in the show.
Which is not to say I'm going to make Aang cheat on Katara or even neglect his kids like in LoK...but keep in mind that by the time of LoK, he's dead. He kind of has to be. So getting to know the 'real' Aang would be something of a challenge. Only his close friends would actually 'know' him, and Korra herself would be imagining her past self as someone great. But what Aang's failings actually be are more subtle sort of things: He would try not to let his achievements get to his ego, but when the entire world thinks your amazing, it's hard not to, and he'd probably need his friends to keep him grounded, but he'd be less likely to listen to anyone who he doesn't personally know/respect, even if they have good advice. This lead to more than once a fuck up on his part. He'd also be somewhat disappointed in Tenzin's way of adapting the Air Nomad ways, which he viewed in a much more lively fashion than Tenzin's more dry, intellectual approach, though he wouldn't say so. You could say that his Air Nomad legacy was a bit of an obsession for him, because he was so anxious to 'get it right' even though it's not possible to replicate an entire culture as he wanted. While he always trusted Zuko, it should also be said that the running of Fire Nation is bigger than any one person, even the fire lord, and he was slightly paranoid of any Fire Nation Politician who even slightly suggested that their imperialism was not a wholly bad approach. And we all know how enraged he gets when someone close to him is hurt. It's hard for me not to believe that there wasn't another situation where Appa or Momo got hurt or died, or maybe even Katara and his kids were political targets. He tends to react...badly in those situations. For himself and others.
Stuff like that. Not explicit "Here is a shitty thing he did without rhythm or reason", but genuine things that instill biases, bad conclusions, poor judgement, etc. Aang was a decent person, but he was a person, and that always comes with faults.
