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.
Alternate Character Interpretation: The author has a great deal of these in delving into the characters' psyches. For example, Zuko has had a hard life, while Aang is unused to having trouble with things, leading Aang to slack off when he runs into trouble with bending training, and for Zuko to show him little sympathy for doing so.
Creator's Pet: The author says that Aang was this for Bryke, and as an attempt to compensate for this by having him undergo hardship, being proved wrong, and not getting together with Katara, which makes him come off as the inverse of this trope.
Die for Our Ship: A less extreme case, but Aang's portrayal in this fic falls into the first(Aang is shown slacking off or wanting to do more frivolous training exercises, and the author openly states in Chapter 6 of Stalking Zuko that she believes that he got Katara as "a prize for being a good boy"), third(suggesting that Aang and Katara have a "maternal" relationship), and fifth(suggesting that Aang is a hypocrite and he's trying to deny Katara the chance to obtain personal closure) bullet points on Avatar's Die For Our Ship page.
Esoteric Happy Ending: The author and Zuko's opinion on the story of Oma and Shu. Oma ended a war and founded a city, but Shu, the man she loved died before she could do that. Since Lu Ten's girlfriend met a tragic end because of her grief over Lu Ten's death, Zuko understands how painful losing a lover can be.
Fanon Discontinuity: Avatar: The Last Airbender - The Promise has been disavowed by the author as she believes that it makes no sense and puts everyone out of character. She admits the series is a good idea but the execution is awful. To varying extents, the rest of the post-Avatar works (the comics and The Legend of Korra) have also been rejected in favor of the author's fanfic, for varying reasons (for example, she doesn't want Aang to get together with the girl he had a crush on when he was 12, nor does she want him to have three kids, only one of whom is an airbender).
Fridge Brilliance: The Earth Kingdom has different attitudes and better understanding of psychology. If the Dai Li are able to have the most sophisticated mind techinques, it implies that they have a good understanding of psychology and how the mind works.
Which is why in Not Stalking Firelord Zuko, Azula doesn't have a true therapist as Dr. Yang has no experience with psychology while in Jet's Troubling Obsession Smellerbee, Longshot and Zuko were able to send Jet to a psychologist.
One that's pointed out by the author, but in Not Stalking Zuko, the scene breaks have a ? between two hyphens, rather than a !. This shows that Katara is questioning Zuko, rather than angry at him.
Fridge Horror: Untrained firebenders in Sozin's comet had their powers increased to dangerous levels...
What kind of power did Ozai to disappear a public figure like Princess Ursa?
The Joo Dees
Especially since it's revealed that Ursa is a Joo Dee.
Fridge Logic: "The Boy In The Iceberg" does a somewhat accurate rendition of Combustion Man's fate (blown up after getting a boomerang to the head), save for the general dramatizing of the scene, such as having Combustion Man give a Final Speech when he never talks. One has to wonder how they knew that if only the Gaang saw the final battle with him.
Informed Wrongness: Aang gets treated fairly harshly by the narrative and the other characters for letting Ozai live, forgetting that 1)he succeeded in stopping Ozai from destroying the Earth Kingdom, and 2)that it's possible to execute Ozai or imprison him while cutting him off from any possible supporters.
Ron the Death Eater: Aang gets portrayed as being highly selfish and immature. He pursues his one-sided crush on Katara and is portrayed as not knowing how to do so without forcing his feelings on her. He's also portrayed as putting Air Nomad beliefs above all else, and is portrayed completely unsympathetically for doing so.
Tear Jerker: Katara having no idea what to do after Zuko is electrocuted and her nearly having a Heroic BSOD over it. Just her helplessness about it.
The entire chapter Deeper Scars.
Unintentionally Unsympathetic: Toph's parents are said to love her, but are very overprotective of her. While they do come around, Poppy's first letter to Toph essentially belittles her, accuses her of being selfish and plays the victim card to get her to come home, which borders on emotional abuse.