Scars
The first time Sokka sees her do it, maybe it's shortly after Zuko's coronation, and he's going to ask Zuko something, but stops when he sees Katara's there. Of course, he'd spy. Zuko's freaking out and flailing his arms, and Katara grabs his sleeve and makes him stop. She puts her hand on his cheek and he calms almost instantly. It never occurred to Sokka to ask how Zuko got the scar, or how it felt, or to try to touch his friend's face. It makes him question if something more isn't there between them, because this moment is so quiet, and more than that, it's intimate. He felt like he shouldn't see this moment between them. So he stayed only a little longer.
Aang doesn't get the big deal when he sees her do it. He knows that they've always had a weird relationship, even after they became friends. Especially after they became friends. But to Aang, Zuko's scar is just skin, no different than a scar you might get if you fall off an ostrich horse. He does not understand the weight Zuko has attached to the scar. To Aang, Ozai is not someone worthy of compassion. Ozai is a vile monster, and Zuko would be better off if Ozai was out of his life. It's hard for him to understand why Ozai is still such a big influence. When he sees Katara touch his scar, he attaches no special importance to it. He knows that no one else touches the scar, but it doesn't bother him. Katara is like that with all of them.
Toph, of course, can't see it. But she feels his heart thud faster whenever Katara does it. Of course, Toph would also know what's really between them, and she'd smile to herself and leave them alone. Second to Katara, Toph knows the weight that scar carries. She also knows the relief that Katara brings him. To be honest, part of the reason she leaves is because she's a little jealous. She doesn't have anyone to touch her scars the way Katara does Zuko's.
Suki would almost interrupt them. Maybe they've all met up on Kiyoshi Island for some reason, whether by circumstance or design, and she's rushing to tell Katara something when she catches them. Maybe it's something as simple as Katara patting Zuko's scarred cheek, and Suki realizes that people don't really touch Zuko. They certainly don't touch his face. Maybe she pays attention a little more, because now she's curious.
Ty Lee would know immediately that something's different. Maybe the first time she saw him when he came home, Ty Lee was shocked and pained, and instinctively reached out to touch it. Zuko did a masterful dodge and made some excuse, hiding it with his hair and leaving. Once, Mai tried to touch his scar, and Zuko caught her hand. Mai never tried it again. But Katara? Of all people, he let Katara touch it, and maybe she saw something in their auras that blended perfectly together, but she knew that this was something only Katara was allowed to do. Maybe then she knew that there was a whole list of things Katara did for him that no one would or could.
Iroh has never touched his scar. He wouldn't try. In the early weeks and months, it hurt him to see his nephew so bandaged. It was a symbol of the shame he felt at not being able to protect his nephew from his brother. He'd promised Ursa that he would watch over her little boy, and now look what happened. When he saw Katara touch Zuko's scar, when he saw Zuko lean into her touch as he laughed, saying she was such a meddler, a little more of the pain left him. He knew that, finally, Zuko had people on his side, people who truly care about him and it's not long before he decides that it's more than Katara's motherly nature that makes her touch his nephew's scar.
Ursa is completely taken aback when she sees her son for the first time since he was a young boy. She does not expect the scar, almost doesn't recognize him because of it. But Katara puts her hand on his face, kisses it gently, and he relaxes. The anxiety and tension lessens, and she sees her son, and her heart twists with a thousand emotions. She tries to touch it, motherly concern taking over, and he grabs her hand before she gets close to it. She learns quickly that touching his scar is a Katara privilege. She can touch and kiss his unscarred cheek all she wants, but she is, under no circumstances, allowed to touch his scar.
Hakoda had always been curious about Zuko's scar. It was such a bad wound, that he wondered how the Fire Lord could let his son be hurt so badly. When he found out the truth, he found himself hating Ozai with a burning passion that was far more personal than he expected. He couldnever imagine doing something like that to his children. He knew the way that Zuko sometimes tried to hide his scar, or the way he'd turn his unscarred side towards people when he talked to them. So when he saw Katara, his Katara, actually touch it, he didn't know what to think. It was late at night, and they were just sitting around talking, but the way she just reached over and patted his cheek was so casual, so routine. Like she'd done it a thousand times before. He wasn't sure to make of it, so he stayed and watched. Zuko closed his eyes as Katara told him he was a good listener, and there was peace on the young man's face. It didn't lessen Hakoda's hate for Ozai. In fact, that just made it worse. But Hakoda knew this was something special between the two of them. Something that would only, always, exist between the two of them.
A/N: This is something that spontaneously happened when I was reblogging a Tumblr thing, and I thought I'd post it here, too, since I'm kinda happy with it, and I haven't posted anything in quite some time. Anywhoo, it's long been part of my headcanon that scar touches are a Katara-only thing, but it was fun to think about how the others would relate to/interpret this. I think, for the most part, they don't think about Zuko's scar. It's just a part of him. I think Toph would really relate to it the most, and because of this, I think she'd be incredibly jealous when someone tries to help him heal his scars, and she doesn't have anyone willing to do the same. With Aang, I think it'd be very complicated. I imagine it being very hard for him to conceptualize the emotions between Zuko and Ozai. Not because he's not mature enough, because I think you have to be a certain type of person to truly understand those kinds of emotions. I can see Aang just going, "cut him out of your life, he's not good for you," and just...not understanding the way Ozai keeps pulling his family back in. All this to say, I don't think Aang would get the emotional significance/weight. Like, he hears why it hurts, but he wouldn't quite get it. Another thing that I'm loving is the Hakoda/Zuko relationship. In my mind, the moment Zuko risked his life to help Sokka break him out of prison, Hakoda kinda adopted Zuko. Also, on a purely parental level, Hakoda's level of Ozai Hate would be dialed up to 11 when he finds out how Zuko got scared. And if the two ever crossed paths, he'd be hard pressed not to deck him. Or gut him. He would not put up with that. I also don't think that, in the end, anyone was surprised that Zuko and Katara were in love.