They showed that when he was interrogating the guy with Rachel Dawes name on his chest. You see some intensity and anger in him that the Joker unleashes.

Also, the plot was strongly influenced by The Killing Joke where the Joker reveals his belief that it only takes one bad day to drive someone to insanity. That deep down, he isn't any different, "he's just ahead of the curve." He tortures Commissioner Gordon in brutal ways to drive him insane, but in the end Gordon stays by the book, and prevents the Batman from killing the Joker. In TDK, they have the Joker succeed with driving Dent mad, but the Joker fails with the citizens on the boat.

So that's why they had Dent turn so quickly, it's a part of the Joker's arc.