The entire scene with Amarao and Haruko in the barber shop. But what really takes the cake is what Amarao says after Haruko deflects and dodges all the bullets fired at her by Amarao's subordinates, who literally come flying through the walls and ceilings to get a shot at her, only to get blown up with her guitar/shotgun.
Amarao: You can't be real.
When Haruko pulls the guitar out of Naota's head, it cuts to Kitsurubami with a nosebleed. Then it cuts to shot of everyone in the Department of Interstellar Immigration, and every girl has a nosebleed.
Let's see. From Amarao suddenly going South Park, to the Lupin III boxing glove, to the Nazi BB gun fight to the aforementioned barbershop scene, all of episode 5. And really, the whole damn thing.
Episode 3: Haruko hits Naota with her Vespa, sending him flying toward Ninamori. The scene goes into slow motion and the camera starts to zoom in on his lips inching closer to hers, with romantic sparkles and stuff all around. Then it goes back to normal speed to show his face smashing violently into hers.
Kamon: What does "fooly cooly" mean? Naota: How should I know? I'm still in grade school!
One particular moment that got this troper was when Naota's grandpa (?) was asking where Canti was, as he sent him out to buy some stuff. Cut to Canti in the convenience store reading an issue of Hustler.
Mamimi's Crowning Moment of Funny comes in Episode 4, when the meteor is coming through the atmosphere: "If that thing comes down here, do you think they'll cancel school tomorrow?"
Naota's dad getting his face sandwiched between the wall and a boxing glove concealed in the unlikeliest of places◊ whilst trying to get sleazy with Haruko.
Canti eating Naota before the battle in Episode 2. And then after the battle, a roll of toilet paper blinks on his monitor and he poops Naota out.
The entire "manga" scene in the first episode.
There's another in the last episode, and when it ends, Naota's dad starts complaining about how much time and money it costs to do a scene like that.
The line "Did she put her tongue inside?" asked whenever Naota gets a kiss/CPR from Haruko.
In the very first episode, there are two extremely long slow-motion shots during the scene in which Naota is hit by the Vespa and then hit in the head with Haruko's guitar, which is then followed by a sudden cut to the Animated Actors talking about how difficult the shots are to make. The complete Non Sequitur of the scene is hilarious.
From the manga, the entire discussion between Haruko and Mamimi after an onconscious Naota sprouts a fleshy horn from his forehead.
Haruko: Good girls wouldn't touch that! Mamimi: How come? Haruko: Ah- well- he's a guy. It's not his fault. Mamimi: Oh. This is... 'that'? Funny. It looked different in the sex-ed video we saw in fourth grade. Haruko: You got a video? Lucky! All I got was a slide show.
In episode 3, when the robot emerges from Ninamori's head, Haruko doesn't have her trusty electric guitar with her, so she grabs the closest thing available: a ukulele from one of the students in the school play. She proceeds to smash said ukulele on the robot's head and hand the neck back to him saying, "Ukulele no good."