Dr Horrible managing to give a credible look of bemusement at Captain Hammer's "gently wafting curtains" line - whilst being strangled, along with an appropriate sound that would have come out as a Flat "What.".
Dr Horrible bemoaning the fact that Operation Heist didn't go as planned at the end of "A Man's Gotta Do": BALLS! Smash to Black.
"Did you notice that he threw you in the garbage?"
"What heist were you watching?"
"The Evil League of Evil is watching so beware/The grade that you receive will be the last we swear!/So make the Bad Horse gleeful, or he'll make you his mare/You're saddled up/There's no recourse/ Hi-ho Silver!/Signed, Bad Horse."
How can you mention Dr. Horrible here without this?
Captain Hammer: She's giving it up. She's giving it up hard. Because she's with Captain Hammer. And these... (holds up his fists) ...are not the hammer.
(He leaves the frame for a moment while Billy stares after him.)
Watch Neil's facial expression during that scene: he's biting his lip, clearly trying to keep from laughing.
Billy gets one just before this, when he learns Captain Hammer is going to stop by the laundromat:
Billy: (tries to look at his watch, but isn't wearing one) Oh goodness, look at my wrist, I gotta go.
Penny: But what about your clothes?
Billy: (turns back, glances in washer) I don't love these. See ya!
Half the exchanges between Penny and Billy at the Laundromat:
Billy: I want to be an achiever. Like Bad Horse.
Penny: The Thoroughbred of Sin?
Billy: ...I meant Gandhi.
Penny: You're driving a spork into your leg.
Billy: So I am. Hilarious.
For me, it has to be the part where Dr. Horrible pauses in the middle of his Moment Of AwesomeVillain Song to correct a cowering reporter on the spelling of his name. After singing about how there will be anarchy... that he will rule.
The look on Hammer's face during this exchange in "So They Say":
Captain Hammer: This is so nice/I just might sleep with the same girl twice/They say it's better the second time/They say you get to do the weird stuff...
Hammer's Fanclub: We'd do the weird stuff!
I found this part particularly funny because it implies that every girl he's ever slept with has dumped/been dumped by him before they could do it again.
Also, pretty much all of the 'commentary'... may I add, the fact they wrote a musical (pseudo) commentary possibly counts as a Funny Moment... but especially the 'sea shanty' exchange.
NPH: Songs can hurt like a fist.
The Tur-Mohel's application to the Evil League of Evil. The application requirements include a minion... so Tur-Mohel has a Minyan (a group of ten adult Jewish males). And that's just the tip of the iceberg.
The revelation of Bad Horse. Admit it, how many of you expected he'd actually be a horse?
"Oh, I'm in pain! I think this is what pain feels like! Oh, mama! Someone maternal!"