I don't understand the confusion, even if you didn't hear what growly-voice man yelled at Gordon.
They explained it at the end... Joker, ultimately, knew that if Dent 'fell', it would throw Gotham into chaos, since he was the white knight. He knew that losing Rachel (especially in that way) would trigger it, and he was smart enough to pick up on how quickly Bats jumped out of the window after Rachel at the party. It wasn't just a 'saving the citizen' kind of thing... it was immediate, he didn't even think about it. Also, he jumped while leaving an entire room of innocent guests with a

ing lunatic. So, he picked up on it.
Joker needed Dent to live, and to lose Rachel. He knew Bats would go after her instead of Dent, so he switched addresses to ensure that Bats would save Dent instead. The gamble, assumably, was that Dent was close enough to get to, and Rachel was never going to be, especially if it was the cops going there, NOT Bats. Either that, or he knew that Bats WOULD make it to wherever he sent him. Doesn't matter either way... the point is that Joker MADE it so Bats went after Dent and that Rachel died, thus ensuring Dent's fall. No confusion... that was his plan, the entire time.
... one of the things that I enjoyed so much about the film was that nearly EVERY question I've seen posed online was actually answered throughout the course of the film. Really, the answers were there... and even if not definitive, there's enough evidence to support EITHER side well (like the is/isn't he dead thing with Dent).