Well, let's hear it. Why is As Good As It Gets so wonderful on narrative and/or aesthetic lines?
Well, I don't have time at the moment for a lengthy disquisition and I doubt anyone would want one, but I will try to make at least five points briefly. Spoilers ahead, though I will try to minimize.
1. First, the most obvious feature of the movie is the unbelievably crisp and evocative dialogue. It's one of those films where half the dialogue or more ends up in the "Quotes" section of its IMDB page. "People who talk in metaphors can shampoo my crotch" is one of my favorite lines in cinema. "I think of a man, and remove all reason and accountability" is brilliant because it shows who Melvin Udall really is -- a man who puts on an air of misogyny as a defense mechanism, and because he is gifted with words, he can be withering and effective, which also makes people not like him and a cycle is created. When the cycle breaks, he turns out to be not so bad.
2. But, importantly, he turns out to be not so good, either. I like movies that defy genre cliches. They are more interesting, more unpredictable, more engaging. It's easy to write a rom-com with a charming, good-looking male lead like Hugh Grant. Writing a rom-com with a misanthropic, OCPD old guy in the lead. And that makes the ambiguous ending so satisfying. In most rom-coms, the couple is painted as living happily ever after, two lovebirds who finally find their Mr. or Mrs. Right.
In As Good As It Gets, Helen Hunt is clearly settling. She doesn't love Melvin Udall. She has come to see through his worst qualities and appreciate that he cares for her in his own way, but he's still a weirdo and it still bothers her even at the end. She's with him because he's rich and he will take care of her and her son. And she manages to cloak that dependence as a form of affection because she needs that to feel OK about herself. Most people settle in some fashion. Our actual mates aren't necessarily all that much like our real mates. We don't think of ourselves as settling, perhaps, because we've pre-settled: we've identified which pond we swim in and have resigned ourselves to the selection it presents. So too with Carol in the movie.
3. The juxtaposition between Simon and Melvin is fascinating. First, Simon -- a gay man with the "gay man habit" of organization -- is the only person who can actually identify with Melvin in some way, as he kind of gets the OCPD. But Melvin is also mean to him and has a powerful anti-gay persona. So they are antagonists, but manage to find some common ground.
The nature of their pain is also instructive. Simon was raised in a good household, with solid parents. If he was straight, he'd have a lovely family -- but they don't accept him as a gay man. That rejection was formative for him and it accounts for much of the pain and shame he feels in the film. Melvin, by contrast, had a terrible upbringing at the hands of abusive parents. But for that reason, he doesn't really care about his childhood. It obviously shaped him, but not in any way that he can recognize, or at least is willing to recognize.
The thing that Melvin can't do is articulate his pain, and that's why he has trouble talking about it, and that's why he is who he is and why people don't like him. And he starts to get it when he sees Carol sympathizing with Simon. Maybe some of that sympathy would be nice, he thinks. But he clearly has no idea how to manage it and so he bombs out. At the same time, it's unclear if he ever gets it all. The line he says when in the car, "it's not that we had it so bad, as much as everyone else had it so good" (this one I'm paraphrasing) reveals his state of mind but it is of course useless to Simon.
4. The common love triangle is replaced by the sympathy triangle. Melvin is really hurt and taken aback by Carol's sympathies for Simon, and he begins to view Simon as his rival (as revealed in the wonderful restaurant scene). Which is quite the twist, since Simon is gay. And that's Melvin Udall's life, full of self-created contradictions that stem from his inability to address his mental condition. The growth of his character is tied to his partial realization of his own responsibility in creating the life he leads, the one he derides as "as good as it gets." But it's still only partial. He's a work in progress.
All of this makes the characters in the film vastly more interesting than the typical rom-com denizens. There is a richness and realism in the portrayals that is highly unusual in a dialogically stylish film of any genre. Tarantino writes great dialogue, but part of that great dialogue comes from the self-conscious unreality in which it is situated. Don't get me wrong -- I love Tarantino. But the premise of Inglorious Basterds is ridiculous, and it's easy to write great dialogue if you're willing to create highly artificial situations (like the basement scene that is correctly applauded as an amazing feat of movie-making, but one that is sort of absurd on its face). As Good As It Gets also has great dialogue without defying realism, so long as you're willing to understand Udall as a man with a debilitating mental condition (that is portrayed with sufficient, if not perfect, faithfulness).
Well, that's four points but many paragraphs so I will stop here. I'm going by memory, btw, so some details might not be quite right. I've seen the film three or four times, most recently about six years ago.