Another very dark example, in the Palace of Justice:
Frollo: You know, my last Captain of the Guard was...a bit of a disappointment to me. (a lash and a particularly loud scream of pain; Phoebus's expression is a mix of 'What the hell was that???' and 'Dear god, was that the guy who came before me??????) Frollo: Well, no matter. I'm sure you'll...whip my men into shape? [grins] Phoebus: (No, seriously, was that the last captain of the guard? Oh god, I'm in trouble.) Um, yes sir, great honour...
Several moments involving the gargoyles are quite funny
Most of "A Guy Like You" (Hugo cross-dresses as Esmeralda, gets his horns stuck in the ceiling, and the gargoyles say Quasi is shaped "like a croissant is", when they mishear a conversation and come to the conclusion that "Frollo's nose is long and he wears a truss" and when they all appear to be sketching Esmeralda, except Hugo who sketches Djali the goat instead.
The epic exchange after Phoebus and Quasimodo decide to go find the Court of Miracles:
Phoebus: Truce? [he pats Quasi on the back encouragingly] Quasimodo: Well...okay. [he hits Phoebus in the spot where the arrow hit him, causing him to groan in pain] Sorry. Phoebus: ...no, you're not.
A lot of Quasimodo and Phoebus' interactions during this period of the movie is hilarious.
The DVD commentary made the previously heartbreaking scene where Quasimodo discovers Esmeralda's love of Phoebus hilarious, with the filmmakers almost MSTing their own movie at some points:
Gary Trousdale: [as Esmeralda] Quasimodo, this is my boyfriend Phoebus. He wrecked his dad's car, can he stay at your apartment for a few days?
Quasi's "cool loft apartment" is a Running Gag through the commentary.
Then there's Clopin, indulging in a bit of literal Gallows Humor:
Clopin: Any last words? [Quasimodo and Phoebus, being Bound and Gagged, can only make some indecipherable noises] Clopin: [rolling his eyes at the Fourth Wall] That's what they all say.
Immediately followed by:
Clopin: Now that we've heard all the evidence— [interrupting himself with a hand puppet] Wait, I object! [as himself] Overruled! [as puppet] I object! [as himself] Quiet! [as puppet] ...Dang.
Then Esmeralda interrupts the "trial" and explains that they are friends, Clopin exclaims in the most innocently bemused voice: "Well, why didn't they say so!?"
"WE DID SAY SO!"
"I'm free! I'm free! ...Oof! ...Dang it."
The entire Esmeralda/Phoebus scene in the cathedral, but especially:
Phoebus: You fight almost as well as a man. Esmeralda: Funny, I was going to say the same thing about you! Phoebus: That's hitting a little below the belt, isn't it? Esmeralda: No. This is.
The part when it emerges that Frollo taught Quasimodo his alphabet using words like abomination, blasphemy, contrition, damnation, eternal damnation, and forgiveness. It's both a blessing and a shame that they stopped at f; one wonders what the rest of the alphabet would have been like...
Absolutely everything in Esmeralda's chase/escape sequence; the best parts would have to be the aforementioned "I'm free!" bit, and Phoebus, after ducking a ricocheting helmet, in dazed admiration: "What a woman!"
The gargoyles building a fully functional catapult from assorted items found in the cathedral and then... shoving it off the roof onto the soldiers.
Victor: "Are you sure that's how it works?"
Made even funnier when the catapult crushes a few soldiers in a manner similar to a mouse trap.
Hugo: Works for me!
"Ah, Paris. The city of lovers is glowing this evening. (blissful sigh) True, that's because it's on fire ... but still there's l'amour."
Clopin spends most of the "Topsy-Turvy" number trolling Quasimodo. At one point he takes part in a chorus line, skirt included!