Sweet Jesus, where to begin? The Joker naturally is hysterical but it's Black Mask that manages to upstage the Joker in hilarity. Every scene with him in it is either him vigorously eating the scenery, him punching his henchmen or him making hilarious faces to bad news. He's pretty much J. Jonah Jameson if he were a crime boss. It also helps that his female assistant never reacts to any of his outbursts.
Black Mask: We're going on offense. Rough up HIS business. Something BIG, something LOUD! When he shows up to shut us down, have a party waiting for him! And when I say party, I actually mean A WHOLE LOT OF PEOPLE WHO ARE GONNA KILL HIM!
Joker: Gotta give the boy points! He came all the way Back from the Dead to make this shindig happen. So; who's got a camera? Ooh, ooh, get one of me and the kid, first...then you and me, then the three of us and then one with the crowbar! Jason: You be as quiet as possible. Or I'll put one in your lap first. Joker: (plaintively) Party pooper. No cake for you.
Also this from Joker again:
Joker: Soooo, are we gonna play truth or dare? I chose dare! (Red Hood takes out a crowbar) Or... maybe I'll stick with truth.
Later, Batman tells Jason how much he'd love to kill The Joker if he had the option, Joker pipes in:
Batman: All I've ever wanted to do is kill him. A day doesn't go by I don't think about subjecting him to every horrendous torture he's dealt out to others and then end him.
Joker: Awww, so you do think about me!
The part where Red Hood is aiming a rocket launcher at Black Mask from an adjacent building and Black Mask spots him.
(Red Hood waves to Black Mask before taking aim)
Black Mask: Oh, hell. (ducks out of screen and runs as fast as he can to the exit)
Red Hood: Wow, he sure can move when he really wants to.
Just after the Joker kills Black Mask's mooks, there's this Dark Humor-filled exchange:
Joker: (pointing a gun at Black Mask) I'm going to need... something to wear. And a very big truck.
Nightwing has several. Of particular note was the bit where he stops to take a sip of tea during a conversation with Bruce. When he looks up, Bruce is in the Batmobile, with the engine running. Nightwing puts his cup down and starts towards it, saying "Could you just once say 'Let's get in the car'?! Is that too hard?"
Which itself is a Mythology Gag to the original comic book story, where Batman does say that & Nightwing's response is "Which one?" as a nod to large number of Batmobiles used in the comic.
*Batman grabs a harpoon gun from Nightwing and runs towards the edge of the building* "So should I...? Do you want me to...? Okay, I'll just... take care of this, then."
"Yes, sir, Batman likes to keep things."
Batman remembering how he met Jason Todd: specifically, returning to the Batmobile to see Todd stealing the tires off the Batmobile.