Does Arthur/Joker grow more sane as the movie goes on?

Question

At the start of Joker (2019), Arthur seems incapable of social communication, of laughing at appropriate times or speaking casually to his coworkers. However, as the movie progresses, Arthur becomes clearly more competent socially, being able to lie to the police officers, convince the Arkham clerk to find his mother's files, and speak eloquently on the Murray Franklin show. Although Arthur does kill increasingly more people, his mental condition seems to improve as time goes on and his uncontrollable laughter even stops.

Does Arthur become saner as he becomes the Joker?

Answer 1

No, he progressively loses his sanity

Although Arthur does kill increasingly more people, his mental condition seems to improve as time goes on and his uncontrollable laughter even stops.

Call me crazy (ha ha), but I would qualify a mass murderer as more insane than someone with emotional incontinence.

As you mentioned, Arthur, at the beginning of the movie, has neurological disorders (uncontrollable laughter) and is socially awkward. That's it. Otherwise he is pretty much an average guy. This is intended so that the audience can relate to the character, and feel pity for him because of how unfair life and other people are being to him.

Arthur becomes clearly more competent socially, being able to lie to the police officers

Arthur has lied before, in fact in the movie he lies to his boss right before the train scene:

Boss: Arthur, I need to know why you brought a gun into a kids hospital.

Arthur: It's a part. It's part of my act now.

If you start from the definition of sanity as behaving abnormally, then Arthur, on his road to become the Joker, clearly goes more and more insane. Not only does he kill people, his murders go from self-defense (kinda), to cold-blooded execution on public TV.

This is him talking to his mother for the last time:

Arthur: You know what's funny? You know what really makes me laugh? I used to think that my life was a tragedy, but now I realize that's a fucking comedy.

He doesn't stutter, or laugh uncontrollably, that doesn't make what he says less crazy. Here is him talking to Murray after confessing his murders:

Arthur: I've got nothing left to lose. Nothing can hurt me anymore. My life is nothing but a comedy.

Murray: Let me get this straight, you think that killing those guys is funny?

Arthur: I do.

Arthur does manage to speak much more fluently on Murray's show than when he did his one man show, which was a similar exercise of being in the spotlight and talking to a crowd, but his newly found confidence is a consequence of his growing insanity: he doesn't feel stress and anxiety as he used to because he doesn't care about the consequences of his actions anymore. What you are referring to as him becoming more sane is actually his growing confidence.

Finally, in the news at the end:

The police led the suspect handcuffed out of the studio

...when asking him what he did...

...merely just a punchline to a joke...

Answer 2

You're misreading comfortability as sanity

Arthur isn't becoming sane. He's becoming more comfortable with who he is.

In the beginning, he at least tries to conform to society to some degree, but he's unable to do so and thus feels unhappy and struggles with things.

But as the story progresses, he starts to move away from behaving like society expects him to, and instead behaves as he wants to. This makes his life easier (by not having to struggle with things he cannot handle), and thus makes him feel happier, and more confident.

The problem is that what makes him happy as a human is essentially by terrorizing others, hence his villainous nature.

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This delves into the whole "insanity is defined by the so-called sane people" philosophy, but the story points out an interesting difference between sanity and mental conflict.

Behaving sane (as defined by so-called sane people) is hard for Arthur, which leads to mental stress. This leads to all kinds of issues for him, such as lack of confidence and a generally awkward behavior.

Behaving "sane" (as defined by Arthur) is easy for Arthur, which makes him feel better about himself, lowering mental stress and improving his confidence and his ability to interact socially (in a way he's comfortable with).

This is true about generally all comic book villains: they think of "good" behavior as ridiculous, and think that their own (different) moral compass is better.