"I'm not going to kill you, but do me a favor. I want you to tell all your friends about me...I'm Batman."
These are the first words that Batman speaks in the film. He's announcing his nature from the comics: that he is violent, but has a rule--he doesn't kill. And this statement also let's the criminal world know that Gotham is his city.
"Jack is dead, my friend. You can call me Joker. As you can see I'm a lot happier."
The Joker emerges fully after he kills Grissom who identifies him as Jack, but is corrected by the newly remade "Joker" after Grissom betrayed his number one guy.
"Tell me something, my friend. You ever dance with the devil in the pale moonlight?"
The Joker asks Bruce Wayne this question before shooting him in Vicki Vale's apartment. Ironically, Wayne has been asked this question before. After Jack Napier killed his parents he asks this question of a young Bruce who stands in front of Napier's pistol.
