The finale which culminates into a slapstick chase when all the remaining cast begins chasing Lum and Ataru, since they remain dissatisfied that Ataru didn't say he loves Lum despite the threat to the Earth and heavy property damage.
The Cameo of Kenshiro Kasumi. First he tells Ataru to shut up with his speech about solidariety with the students who didn't do their homework and were keeping the students in class after school, only to be reminded he didn't do his homework too. Then Kotatsu Neko enters in the class, and Kenshiro promptly picks a fight with him... And takes all of five seconds before being utterly defeated and sent flying into the wall.
Chapter 39, "The Curse of the Copy Man". An accident with an object-copying machine results in a "Freaky Friday" Flip of sorts between Ataru and Mendo's physics notebook. Notebook/Ataru looks like Ataru, but has the page contents written all over itself, is incapable of doing anything other than repeating verbatim the words and actions of anyone who talks to it (because "all a copy-person can do is copy what he hears"), and peels apart into "pages". Ataru/notebook (Ataru's consciousness trapped in the notebook) loans these "pages" to the other students, prompting Mendo to remark: "I never thought you would stoop to selling your body!"
The climax of the second movie when Ataru calls out for every girl in the series who had appeared up to that point, including unnamed one-shot characters and his own mother, before finally calling Lum's name and waking up from his dream.
Lum uses a device to make a copy of Ataru in order to thwart one of Ran-chan's plans. The copy can be easily distinguished from the original Ataru thanks to the prime symbol floating next to his head. Long story short, countless copies of Ataru, each one with his own prime symbol floating next to his head, end up running amok all over town.
Reversed in another episode when Ran-chan stuffs Lum into a xerox machine to make exact copies of her. Long story short, Ataru ends up with hundreds of Lums all pining for him by the end.
Oyuki is tasked with playing the goddess Amaterasu for a class play but gets sick at the last minute. So of course the real goddess Amaterasu shows up and ends up getting dragged into it.
The episode where Benten decides to see why Ran is utterly terrified by the calm and collectedOyuki by getting her angry. When she finally succeeds at getting her angry at one of her pets, Oyuki gently scolds him... While freezing Ran's home in the process and nearly freezing and impaling Benten, Ran and Lum to prevent the pet from escaping by accident. It ends with Oyuki still scolding her terrified pet while Ran and Benten are trembling in fear.