Kawazu impersonating not only the voices of Tsukiko's jealous coworkers, but their makeup.
In episode 2 Ikari, fed up with Tsukiko's vague answers, starts questioning Maromi. And then:
Tsukiko: Is he brain-damaged? Ikari:(going beet red)Wha—!? Tsukiko: I mean Mr. Kawazu. Ikari: ...(in the stiffest tone imaginable) he's in...stable condition, thank you. Maniwa:(choking back laughter)
The entire Running Gag over the bet between Ikari and Maniwa when they debate the validity of Tsukiko's story. Ikari believes she's lying, Maniwa suspects there's more to it; they decide the "loser buys dinner".
At the end of episode 1, after Kawazu is attacked:
Maniwa: Hey, Chief? I think I feel like Korean barbecue tonight.
In the final episode, when Maniwa finally discovers the truth about Lil' Slugger and Tsukiko's connection to him.
Maniwa:(To Ikari) Looks like we're splitting the bill!
Taeko's happier memories with her father, in one of them insisting that she marry him someday. Her innocence when she makes such a suggestion is what makes it bizarrely amusing.
Later comes around as a massive Tear Jerker when she discovers what kind of man he really was under that friendly exterior.
"Happy Family Planning", which manages to make suicide funny.
If this episode were the basis of the whole anime, it would be the single funniest anime ever.
The little girl's face when the old man suggest various ways they can die.
This episode is notable for being very disconnected from the rest of the series, since it focuses on a new plot that has little to do with the main narrative. So it comes off as hilarious when the old man brings up Lil' Slugger sixteen minutes into the episode, as if the show was reminding you that you were still watching Paranoia Agent.
Old Man(casually): Speaking of which, remember Lil' Slugger?
The best part: when they're at the lowest, the suicide group wonders if Lil' Slugger might be able to kill them. Their despair summons him... and then when they cheer up, he freezes up and runs for it (the lack of anxiety, possibly combined with them being dead already, throws him off). So they chase down Lil' Slugger.
In his haste to get away Little Slugger tries rollerblading down the stairs and falls on his butt.
When they're about to jump in front of a train. The guy who jumps before they do actually gets off the tracks, muttering about how much that hurt, and how hard it is to die these days. Even better-his suicide attempt actually worked.
Their failed attempt at hanging themselves (which, sadly, is cut from the UK DVD version out of fear of imitation)
Finally, after they realize they were dead after the first try, their first action is to...photobomb a bunch of girls, walking off happily as they ladies they pranked scream in horror.
Then there is the episode "Etc."; several of the stories told by the Gossipy Hens are hilarious.
Mainiwa's Sanity Slippage starting with him innocently roleplaying with Kozuka to get info and ending with him taking on the role of the Old Man right down to narrating the final On the Next scene.
