Batman Saving Dent over Rachel
I've seen this movie a bunch and was confused on this until recently. After Joker tells Batman the locations of the two, Batman tells Gordon he was going after Rachel, Gordon is going to try to save Dent. I had thought that Batman lied to Gordon because he feared he wouldn't get to Dent and time and wanted to make sure somebody would be able to save him because Dent was that important to Gotham.
What really happened is Joker lied to Batman, he switched the locations of Dent and Rachel. Joker knew Batman had a thing for Rachel so he purposely mixed up the locations. Joker wanted Dent alive and knew the Gordon wouldn't get to him in time so he mixed up the locations so the Cops were actually trying to get to Rachel. Joker knew Batman and Dent both cared for Rachel, so it would potentially break both of them.