Subtlety was always the strong suit of Avatar: The Last Airbender, and Zuko's path to redemption proved that more than anything. Taking the character on a journey from a villain hunting down the Avatar to restore his honor, to one befriending the Avatar in order to restore balance to the world, everything about Zuko indicates a rich and multifaceted character who inhabits a complex world. In fact, one theory contends that even an integral aspect of Zuko's design hints at the depth of detail in Avatar's conception.
Zuko's scar already carries potent symbolism for Zuko's struggle between good and evil, but it also may indicate just how sinister his father Fire Lord Ozai was. Did Ozai deliberately control the placement and degree of Zuko's scar as an act of punishment?
Zuko's early arc is marked by his desire to capture the Avatar on behalf of the Fire Nation, and in the early episodes of the series, the audience learns that the mission is an opportunity for the banished prince to restore his honor. After speaking out of turn in front of his father, the Fire Lord challenged the young prince to a duel known as an Agni Kai. Although Zuko refused to fight his own flesh and blood, Fire Lord Ozai scarred his son forever with a distinctive burn to the face Zuko could never forget. The story is enticing in its own right, but a recent fan theory suggests there is even more detail to the scar than many fans could realize.
According to the theory, Zuko's scar is so severe that he likely should have been blinded and deafened on that side of his face, but that Ozai's control was so absolute that he deliberately allowed Zuko to retain those senses in order to fully take in the shame of the lowest point in his life. After all, the very fact of Ozai's participation in the Agni Kai was meant to be a lesson to Zuko in the first place. The Fire Prince's insult was taken by the traditional customs of the Fire Nation to be an insult to the Fire Lord directly. In ending the Agni Kai even when Zuko refused to fight, it would have been important for Ozai to impress his lesson on his son as fully as possible.
There is speculation among fans about whether or not Zuko's hearing and sight are impaired by the scar, although the question does not come up directly throughout the franchise. Indeed, Zuko's scarred eye has at least some level of sight remaining, as it tracks objects perfectly well alongside its companion, and there are notable instances such as his fight against the Rough Rhinos where he detects the approach of an arrow from his scarred side swiftly enough to intercept it after it was fired. Zuko's senses seem fully intact, so Ozai's control in scarring him must have been lethally precise.
This detail not only speaks to Ozai's cruelty, as it shows just how intentional and in control he was during the administration of his lesson to his son, but also speaks to the Fire Lord's impressive firebending. Very little is seen of Ozai's firebending throughout the franchise, and indeed, in almost every instance, it appears to be less impressive than other firebenders such as Iroh or Jeong Jeong. Showing that Ozai could not only scar an opponent, but to do so in such a particular and precise way, stands out as an exemplary display of the Fire Lord's talents unlike most he ever showcased.
The symbolic value of Zuko's scar stands out as potent throughout the series, often used to represent the duality that haunts him as the prince is torn between honoring the legacy of his family and changing it for the betterment of the world. Such a detail would add an extra layer not only to Zuko's character but to Ozai's as well.
Ozai could certainly use it, as the villain has little screentime or depth throughout the three seasons of the original series. Not even fully appearing until late into the series, much of the primary antagonist's characterization comes secondhand through other characters and his own reputation. Such subtle details as the intentionality of Zuko's scar stand out as indications of just who exactly it is that Aang needs to take down in the series finale, and it's a detail that's present from the very first episode of the show.