When Captain Battleship is introduced to his Quirky Miniboss Squad, the Battleship Five Quartet, he notices that it has six members. So he opens a Trap Door and drops them out of his vessel. When an advisor calls him out on it, he opens a Trap Door under himself and falls out as well.
Not in the original manga or the anime, but the PS2 game (which actually came before the anime and had a mostly different voice cast) features a scene (starts around 4:01) of Bo-bobo's head popping out of a door on Softon's crotch. Words can't describe just how bizarre and hilarious it is.
Hatenko's weakness: Defeating him would... defeat him!
Turns out that this is Dengakuman's weakness as well.
When Lambada uses his Super Fist of Polygon to transform into Don Patch and Jelly Jiggler, Bobobo manages to hit him but attack both the real one and the fake. Also, it turns out that Bobobo was aiming for the real Don Patch all along.
The entire Humiliation Conga against Lambada, where Bobobo takes him into old-style video games, is hilarious.
From the same episode, the definitions for the term polygon. And Beauty's reactions.
Beauty eventually gets fed up with it and gives the PROPER definition. Naturally, she confuses everyone with the complicated definition.
The narrator's chatter in various episodes. The characters tried to remind him of the events in the previous episode for the recap, he complains about his pay being cut for each time he drifts off-script, and the main characters defend him when some villains make fun of him. This is made even better when you learn that, in the original Japanese script, the narrator only... narrated. He was given a personality and these lines in the English dub.
Beauty's horrified reaction to the idea of Bobobo being transformed into a schlub during his fight with the Mean Green Soup Alien.
Schlub Bobobo: I got this soy sauce on sale! So then the Principal says "Spank you very much!" Get it!? Spank you, instead of thank you, HEHEHAHA! I got a million more jokes like that one! Hey, the ladies call me "Don Juan," because they Don Juant to be around me, HEHEHAHA!
A moment in episode 28 when Gasser shows concern for Jelly Jiggler.
Jelly: You're worried about Jelly like me?
Gasser: Huh? Of course, we're family, right!?
(An image appears in Jelly's mind of a group of mobsters gambling.)
Gasser: Not that kind of family!
Everyone's reaction to Torpedo Girl's reveal is being so blasé about it compared to how normally over top the reactions usually are.
Bobobo's temper tantrum at the train ride in episode 13.
Bobobo: Hop aboard, let's go for a ride!
Beauty: Huh? You know, I'm gonna wait this one out, maybe I'll catch it next time around!
Bobobo: WHA!? You're not coming along?
Bobobo: BAW HAW HAW I DON'T WANNA GO ON THE CHOO-CHOO BY MYSELF I COULD GET BAMBOOZLED BY A MONKEYS!
Beauty: Take it easy!
Bobobo: I COULD SLIP ON BANANA SKINS AND MY BOOT HITS THE CONDUCTOR WHO BOOTS ME OFF THE TRAIN AND I HIT THE RAIL AND SCRAPE MY HEAD AND MY HAIR CATCHES FIRE ALL BECAUSE YOU WOULDN'T COME WITH ME! Nevermind, I only bought one ticket.
Beauty: You could have told me...
In the same episode, the train Bobobo is riding on disappears into a small tunnel. Beauty wonders where they've gone...suddenly, a gigantic baby bursts out of the tunnel.