Re: Stuff you like to believe happened in Nolan's series
Well, concerning Dent, he was who put in jail all of those criminals with the RICO case. After that, the mayor tells him that everything will be onto him, everyone whose interests would be put in peril would try to find a way to bring Harvey to the ground. Basically, because of the singularity of his deeds, if anyone gets anything onto him, all of the criminals would set loose.
And as for Gordon, isn't allowing a vigilante to roam the city rooftops a little dubious too? But as you say, it takes a toll on Gordon and on Batman too. The point of the action is that they don't get away without consequences. They put their souls on the line to protect the city. As I said before it's a sacrifice, and that's perhaps more than heroic.
A hero can be anyone. Even a man doing something as simple and reassuring as putting a coat around a young boy's shoulders to let him know that the world hadn't ended.