And he should be dead. It would completely destroy the end of TDK to have Harvey live. Besides, what would Two-Face even do in a sequel? His whole plot was wrapped up quite nicely in TDK, what could he do in the next movie that would be new or original?
I disagree, I don't think it would destroy the end of TDK.
You could do a number of things, one, you could have Gordon realize Dent's alive and secretly lock him away in Arkham, and then tell the world he's dead. Two, you could have Gordon realize Dent's alive, and have him immediately carted off to a secure hospital, telling everyone that Batman attacked him. Gordon could also tell the nurses and everyone else that Dent was suffering from extreme grief from the loss of Rachel, and to discount any of his rants, because of the mental state he's in at the moment.
If you go with the first option, in the second movie you could have Dent escape, out for revenge against Gordon and Batman. He could discredit Gordon's good name by revealing all he had covered up, and at the same time try to build a criminal empire to take over Gotham.
If you go with the second option you could have Dent trying to be rehabilitated. They could repair his face, and he could be shown as trying to help himself. He can't do it, and rescars his own face, then again goes out to discredit Gordon by revealing that the Batman didn't kill anyone, but he did, and also have him try to build his own criminal empire.
One big plus (either direction you go in) is that we could explore the duality of Two-Face more, because we didn't get much of it in the movie. We could show case that he actually has a split personality, and better outline the difference between the two, and show how he is
absolutely dependent on his coin. We kind of got that in the movie, but it wasn't completely established.