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Whenever Neko, in her cat form, starts yowling. She's just the tiniest little kitten trying her hardest to look intimidating.
Yashiro's nonsense-spouting in an effort not to be killed.
Yashiro: But I'm innocent!
Kuroh: *points him to the video showing him clearly guilty*
Yashiro: W-Well, maybe I don't look innocent... but you know what they say, right? Don't judge a book by its cover! It's what's on the inside that counts!
At the end, when Kuroh closes his eyes in his usual cool and composed manner, the viewer realizes that Neko has drawn eyes onto his eyelids, making him look ridiculous. The background music even stops abruptly for comedic effect.
Kuroh running through the wall Neko created only to crash into a real one.
Episode 3: When Misaki and Rikio crash into Izumo's bar get in a fight and promptly get their skulls crushed by said bartender. After Misaki explains what he and Rikio were fighting about, he resumes fighting while dangling in midair. It's only when Rikio and Misaki apologize to the bar that Izumo clears up the misunderstanding.
Kuroh taking a break from trying to kill Shiro... and eating a meal with him and Neko.
Kuroh: *sips drink* Okay, time to kill you.
When Yashiro's cleaning robot gets buggy and first mistakes his bag as trash, and when Yashiro tries to retrieve it, it recognizes him as trash and tries to throw him away too. This, however, turns out to have actual plot significance...
Yashiro explaining things he got from Kuroh as being from "his wife", with Kuroh threatening to cut out his tongue.
Yata and Kumamoto dramatically prepare to enter Ashinaka High School to find Yashiro - only to be stopped comically at the gate because they don't have passes.
The beginning of Fushimi and Yata's Drama CD - Fushimi was the interviewer and Yata was the interviewee, but the former ended up answering most of the questions for the latter, many of which even the latter did not know himself (e.g. his current height).
In fact, every time they interact without fighting is just hilarious. Special mention goes to Saruhiko signing up for the hero show Misaki works at because he is bored. He then blows the show and bickers with Misaki about how HOMRA doesn't pay taxes, SCEPTER 4 is a bunch of weirdos, the importance of drinking milk, eating vegetables and that Misaki's monster costume has a "height limit". Except for the end, it's hysterical.
Episode 8: Seri drowns a traditional Japanese sweet with disgusting-looking red bean paste, making it look disgusting. She then serves it to Munakata, who doesn't want to eat it, but being the polite guy he is instead of out-right rejecting it he sets it aside when Seri's not looking. When Fushimi arrives Seri asks him to come sit next to them. Once Fushimi sees Seri's surprise dish he replies that he's fine standing where he is.
Radio Drama 2:
(At an arcade)
Yata: Which one do you want to play, Anna?
Anna: Which one... is red?
Yata: How about that one zombie game? There will be 'red' coming out once you shoot them!
Anna: I'll play that.
Totsuka: Anna's clothes have really complicated designs... Can I take a look?
Totsuka: O-OUCH!!! Yata, why did you hit me?!
Yata: Weren't you peeking under her SKIRT?! Are you a lolicon?!
Totsuka: I wasn't peeking! What a terrible thing to say about other people! I was just picking up the frills on the top! Don't imagine such weird things... Aren't you the one who's a lolicon?!
One of the Green Clansmen is a masked man who can manipulate surroundings; this includes walking through walls. After Anna is kidnapped, Fushimi shows Munakata surveillance footage of the incident and Munakata keeps calling the clansman a ninja, much to Fushimi's dismay.
Fushimi looping the footage of the Green clansman walking through the wall, over and over.
On a similar note, other characters make fun of the Green ninja clansman as well. One character even calls him a "cosplay ninja".
Yata skateboarding and kicking ass inside the Gold King's tower... until he runs into a sign with an attractive busty girl on it. He is so flustered he loses his balance and falls off his skateboard.
Neko and Yukari's parrot having a petty cat fight.