Upon hearing someone refer to Batman as "insane," he remarks to Bruce, "What rot, sir! Why, you're the very paragon of sanity. By the way, I've pressed your tights and put away your exploding gas balls." "Thank you, Alfred."
And then there's this:
Batman: You think you know everything about me, don't you?
Alfred: I diapered your bottom, I bloody well ought to... sir.
The Joker is terrifying in this movie, but he does get some of the best lines. Hell, even his Dynamic Entry is amusing:
Joker: (after shooting up the singing machines) I hate that song! (he sees Salvatore Valestra) GASP! Can it be?! Old Sally "The Weezer" Valestra! Welcome, Pizon! It's been a dog's age!
Sal: (visibly nervous and sweating) Hello, Joker. Didn't mean to drop by unannounced.
Joker: Nonsense! Mi casanostra es su casanostra! (shoves him) So what's an old timer like you want with a two timer like me?
Sal: Business. I've got—
Joker: (runs over, ecstatic) Ooh, business! Sounds like fun! (shoves Sal into one of the rides) Come! I've prepared a more comfortable environment. Now, hold onto your hat and watch those valuables (slams the safety bar into Sal's crotch!). It's going to be a bumpy ride. (cue maniacal laughter)
He gets one more when they arrive at his "humble abode".
Joker: (sees his tiny robotic dog at his feet) Don't mind my home security. Down, Rusty! (field goal kicks the dog off screen) Can't be too careful with all those weirdos around!
He gets a third Dynamic Entry after Arthur hangs up with the police after they failed to capture Batman:
Joker: (standing in the doorway, framed by lightning flashes) Tsk, tsk. To think our tax money goes to pay those jerks.
This troper is both terrified and incredibly amused by Joker's line the second Arthur's done on the phone with Andrea;
Earlier, when the Phantasm confronts Sal in his home, only to see how the Joker's killed him and strapped a camera to his lap (in addition to oodles of high explosives)...
Joker: Whoops! Guess the joke is on me, you're not Batman after all. Looks like there's a new face in Gotham and soon his name will be aaaaall over town...to say nothing of his legs, and feet, and spleen, and head...[KRAK-OOM!]
Then there's The Joker's lack of surprise when The Phantasm arrives, when he's "hitting" on Hazel.
The Joker:(annoyed) Isn't it just the way? You get in the mood, and company shows up.
Most of Andrea's lines are amazing, mostly due to her being a great Deadpan Snarker.
Andrea: (watching Bruce practice martial arts) What is that?
Bruce: (glares at her)
Andrea: That was a joke.
Bruce: Jujitsu is no joke. It takes years to master. (Andrea walks over, grabs his arm, and executes an awesome shoulder throw) HEY!
Andrea: Got a few moves of my own. Miss Hovey's self defense class for girls.
Andrea: (offended) He laughs.
(Bruce trips her and pins her)
Andrea: Nice foot work. Can you dance too?
(Bruce smiles and they kiss. Alfred starts to walk over with drinks, notices them kissing, and quickly exits)
Made even better by the fact it turns into a brick joke later on in the film's present. Alfred really has no sense of timing.
Arthur pulls a dick move by bringing up Andrea and Bruce politely dispatches him afterwards.
Bruce: Thanks for the handkerchief, Arthur. You know where you can stick it. (shoves the handkerchief into Arthur's breast pocket)
Likewise, his meeting with Sal. What should have been a conversation that ended with the old man chewing Arthur out (which he sort of did), Arthur instead winds up making Sal's cabbie pull over, and zinging the old man, which still probably has some connections in the Gotham underworld and leaving him flabbergasted. The "What the fuck just happened?" look on Sal's face just sells it.
The Joker's initial reaction to Saul's cash offer to off Batman.
The Joker: ... (yawns) What do I look like, pest control?