Mmm, I distinctly recall him saying that he won't stay _as long as the machine exists_, to which Bruce responds that when he's done he should type his name; and then when he does at the end, it's accompanied by Gordon's voiceover saying how people deserve to have their faith rewarded sometimes.

So I think he didn't resign because he didn't need to.

I'm pretty sure the last we see of the Joker is the SWAT team coming to where he's dangling, because I was waiting for something else too.

I really hate the idea that Dent might not be dead, but more on that in response to genarti.