Any episode centering on the Kurosawa Detective Agency. In 7 and 8 alone we have Gai's fear of cats and deciding that suspecting Li is just him being paranoid, the development of Kiko's crush, Mao's misadventures (including possessing a raven, heroically snatching the MacGuffin, and... immediately running face-first into a wall), "The starsare sobeautiful...", and the Brick Joke inherent in the missing cat itself.
As Kurosawa is carrying Mao in a pen, he remarks that he's inclined to drown the cat. Quoth Mao:
At the beginning of Episode 15 we have November 11th's answering machine message.
"Thank you for your call. You've reached Jack Simon. I'm sorry, but I can't answer the phone right now. As compensation, I have a joke for you..."
The middle section of Episode 17, from a great example of the Cover-Blowing Superpower trope to Sakurai idolizing Hei and concluding that his Big Eater ways and being Chinese are the true cause of being a martial arts master to the landlady forcing them to replace a door after Sakurai's attempted Dynamic Entry, and then bonding over drinks afterwards.
Several points in Episode 22. First, Mao's inner monologue about how Contractors do the rational thing, and what to do when he's surrounded by enemies. Then, he looks up and goes "MEOW?" Then, later, Dr. Schroeder asks if anyone in the room is "normal", and Amber says that they're all Contractors. Schroeder sighs and says, "Then I guess the cat is my only friend." To which Amber replies, "No, he's a Contractor, too."
The Last Episode! After winding up the storyline in the 25th episode, the Last Episode is pure comedy gold, and well a last look at a few dead characters.
Yin spouting besitiality fanfiction from memory was hillarious.
Mao's battles with horny cats.
The references to Hei's extremely sexy collarbones.
The conversation between Misaki and Otsuka is all too hilarious in the OVA.
Misaki: "It's BK-201, the Black Reaper himself."
Otsuka: "He's the guy I've been stalking?"
Misaki: "You didn't know he was the Black Reaper?"
Otsuka: "No. I thought he's a sexy guy with a great body."
And then there's the Friends of the Gate. They want to recruit people to their cult. Hei just wants to put away his groceries.
From season 2, two Japanese girls talking to Ilya: say "Do you speak Japanese?" in perfect Engrish.
It's hard to tell if it was meant to be funny, but Ilya scaring them shitless with his drawing of them as mutilated corpses, without dropping his friendly smile, comes across as pretty funny in a Crosses the Line Twice kind of way.
Hei is fighting Genma, whose power is to manipulate metal, and he uses it to turn large chunks of his truck into Instant Armor. Then, Hei jumps onto a car as it's driving away, and Genma turns to the truck to chase, and realizes that he's wearing most of the truck, and the rest is in shreds. Whoops.
And the woman and her child in the car. Mom, is there a contractor on our roof?
Episode 8 of the second season: Hei's overeating habits return, shocking everyone in the dinning car, including the Russian Col. that was trying to recruit him. Meanwhile, Mao is seen trying to hide from a conductor, complaining that "This is turning out just like a cartoon I once saw!"
At one point in the Interquel Manga, Hei runs into Eric Nishijiima's father who rants at Hei about the events at the end of the anime. Hei's response? 'I don't need you, go away', said with a completely straight face. Cue the rant shifting to how rude it is for someone to enter someone's home and tell them to go away.
During Hei's last battle with Wei,
Wei: Do you know how humiliating it is to be defeated?!