I feel like the biggest elephant in the room for Melvin (Jack Nicholson) is that he is for sure autistic. Aside from the apparent OCD and germaphobia, he can’t relay emotions, struggles to make eye contact, has no filter, and is very matter of fact. In ‘97, we didn’t talk about being on the spectrum nearly as much as we do now, but it seems pretty apparent. This could help explain his terrible mannerisms or his abrasiveness in the outside world (it does not explain, however, his insane bigotry). So with all of that being said, there’s no way his relationship with Carol (Helen Hunt) works.
TO CLARIFY I am not saying that autistic people cannot have a functioning relationship with people - they do every single day. What I am saying is that this character, specifically, will not be able to make this relationship work. Carol is an older woman at her wits end and she just wants something simple and stable after having to deal with all the shit with her ailing son. Melvin, while seeming like somebody who actually does want to care and be better, will not be able to fully comprehend when to just let things go, or for that matter, not say anything at all. Sure, it may seem cute at the end of the movie, but realistically, he is going to make Carol snap more often than not. They are two different people in two different places in life with very different versions of what they want. This relationship will not work in the long run.