Anvilicious: Averted, for the most part. Despite absolutely crappy lives, mostly of their own doing, no one really gives anyone a 'Suck It Up' speech. The three main characters are their own worst enemies, effusive and self-destructive (and in Simon's post-hospital state, self-loathing)
Simon: Thank you, Melvin. You overwhelm me. (beat) I love you.
Melvin: I tell ya, buddy, I'd be the luckiest man alive if that did it for me.
Also, the scene in the main page's picture when Melvin picks up Verdell and everyone around him smiles as he showers affection on the dog. It's also a Crowning Moment of Funny, because he's doing that out of happiness that he'd trained the dog to avoid stepping on cracks.
Melvin's second compliment to Carol, which manages to blow away his his already amazing first one. ("You make me want to be a better man.")
Melvin: I might be the only person on the face of the earth that knows you're the greatest woman on earth. I might be the only one who appreciates how amazing you are in every single thing that you do, and how you are with Spencer... "Spence." And in every single thought that you have, and how you say what you mean, and how you almost always mean something that's all about being straight and good. I think most people miss that about you, and I watch them, wondering how they can watch you bring their food, and clear their tables and never get that they just met the greatest woman alive. And the fact that I get it makes me feel good... about me. Is that something that's bad for you to be around?
Despite having no romantic interest in Carol, Simon gives her an amazing compliment that jump-starts their friendship almost immediately: "You're why cavemen chiseled on walls."
Melvin tries to cheer Simon up by claiming that the dog only likes him because he keeps bacon in his pocket. And then the dog runs to him, ignoring the bacon Simon is holding, ruining the effect.
Fridge Brilliance: Look closely at any scene when Melvin starts acting like a jerk. It's usually when someone has interfered with his routines or compulsions.
Jerkass Woobie: Melvin. Even when he tries to be helpful, either in his own abrasive way or actually doing something kind all on its own, no one is ever grateful to him, they all treat him terribly because his mental illness bothers them, and they constantly demand he stop being so rude and confrontational to others while they feel no need whatsoever to be anything but horrible to him.
...then, after she rushes madly to her apartment to find that the doctor is there to her son, but nothing is particularly wrong with him at the moment, she is informed that the paediatrician has been sent to attend to her son by Melvin... a really creepy jerkass customer from work who has come dangerously close to being a stalker.