Okay, I've been out of this thread for a day or two, and the discussion has moved along, so I'm happy to drop almost all of my previous ongoing debates. However, I wanted to follow up on something, because it struck me as even odder than all the rest of @Anwar 's arguments.
To set the stage, when I pointed out that contrary to what he had claimed, Arthur doesn't get violent with Sophie on-screen, to which he then claimed that it was later implied that Arthur had killed her. When I asked how, this was his answer:
First off, no. Not obvious at all. At least not to me, as the thought hadn't even crossed my mind until some people brought it up afterwards. Which brings me to second, that's not an answer. Please, do point out to dimwitted old me where and how the movie implied that Arthur killed Sophie.
He walks out, police sirens are blaring.
Pretty obvious what we'd get from that. Not showing it on-screen was just a manipulative way of keeping our sympathy with Arthur because the movie refused to own up and show we'd been cheering on a nutcase doing bad things. Showing him kill Sophie would have killed that sympathy. As opposed to Falling Down, which had the intelligence to deconstruct D-Fens at the end.
And then the director has to outright say "He didn't kill her" because he didn't have the courage to follow through and say "Yes, you were cheering on a murderous nutter." and instead went "Oh, don't worry. He didn't kill anyone who didn't deserve it one way or another, he's a good guy!"