Uhm...
It\'s kinda obvious what happened.
The Joker switched the addresses. It was a "joke". You know? The Joker knew that Batman had feelings towards Rachel, he even told Batman he knew it. So, he could easily predict, that Batman being human, would go to rescue the girl he cares about over Dent. So, by switching the addresses, he allowed Batman to , in a not direct way, be responsible for Rachel\'s death.
Look at it this way. Weigh the two people. Who is more important? Dent or Rachel? Dent, he is the upcoming D.A . So, in hindsight, Batman should of rushed for him first, but he was in love with Rachel and it was obvious to the Joker. So - what\'s the best thing to do? Make it so because of Batman she died.