Tons of these (such as the entire finale), but episodes 7 and 8 take the cake, with the rivalry between Lunar and Sun actually starting a war, which is resolved with a suitably epic sing-off. Then throw in Saru, who pulls off the most epic use of A Storm Is Comingever. The whole deal is topped off with the revelation that Maki was not attacks by Lunar's bodyguards. Maki attempted to attack them by launching herself will her shell gun, missed, and pancaked into a wall.
Mawari and the rest of the school's female population storm the school during Sun and Lunar's singing contest. They stop when Mawari sees a crazy fan.
The entire episode where Lunar and Sun's fathers try to "understand" them by playing gal games and then cosplaying as schoolgirl cliches is made of gold (Sun's father dressed as catgirl is not something easily forgotten) but there's one particular gem of a line at the beginning, when Lunar's Dad is talking about Nagasumi about how to make Lunar happy. Lunar's dad remarks about how Lunar is so pitiful and miserable (she had to miss a school trip and is depressed about it), and Nagasumi suggest that he cheer her up somehow, suggesting that her father take her on a trip. This results in Lunar's dad bursting through the window and greeting Lunar with this:
Lunar's Dad: Lunar, you are pitiful. Let us go to Dubai.
Sun hitting Lunar and then Kai with volleyballs without even trying.
Sun imitating other people's laughs.
Furiyo dressing up as a human girl named "Brittany".
Sun and Lunar turning an all-out gang war into a dance party.
One episode has Nagasumi drinking a potion to increase his popularity, causing all the girls in the series to see him as what their ideal man would look like, including Mawari seeing him as a defenseless grade schooler and his mom just seeing Masa.
Sun agrees to pretend to be Lunar's boyfriend to help her prepare for a soap opera role. Cue her shifting into a more musclebound, macho persona and taking the term "beard" a little too literally.
Sun and Akeno's epicLes Yay in the bath on a school trip. The short version is that young mermaids revert to their mermaid form when their legs get wet, so Akeno and Sun reserve a private bath so they can train themselves to resist the transformation. Naturally, their dialogue sounds like they're doing something completely different, which nearly drives both Nagasumi and Mawari insane as they listen. The best part is that while Nagasumi figures out what was really going on, Mawari, who's not in on The Masquerade, never gets the true story, and for the rest of the series thinks that Sun and Akeno had sex during the trip.
In the episodes flashing back to Masa's past, he is shown to be a regular/white man with waist-length hair instead of a black guy-complete-with-afro.