These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Alternate Character Interpretation: Naota's older brother. Is he a giant asshole that left everything just so he could be a baseball player? Or is he a nice guy who just isn't good with people?
Is he a giant asshole or did Mamimi just completely overestimate their relationship?
Gateway Series: The soundtrack acts as the perfect gateway to The Pillows. As a gateway series to the genre of anime however, it's probably not the best choice (unless you're one of those people who believe that Japanese cartoons are weird and/or sexually deviant, and you need proof of this for your friends).
Episode 5: Haruko surfing on (in midair) and using a bass guitar to take down a multi-story five-armed gunman robot that's actually a giant hand (each "arm" is a finger) - while wearing a Playboy Bunny suit. That's not something you see every day, folks. The end of the series counts too.
Haruko wearing a Playboy Bunny suit during that batshit insane battle is actually a reference to one of the opening videos a group of amateur animators made for DAICON in 1982 and 1983 before they later formed Gainax. To drive the point home, Haruko even shouts "Daicon!" in that scene.
When Amarao opens fire on her in the barbershop, Haruko wields a razor and slices each and every bullet perfectly in half without effort. Cue dozens of Men in Black with machine guns storming the place, and Haruko proceeds to defeat all of them without breaking a sweat.
Episode 4: Naota saves the city from a hand-shaped robot satellite that falls from orbit and pitches a gigantic baseball-shaped bomb at the city, using an electric guitar that Haruko pulls from his head to bat it. Yeah.
Let's be honest: the entire series has an absurdly high HSQ.
Moral Event Horizon: Haruko feeding Naota to the Terminal Core, probably expecting that it would kill him, and knowing for certain that doing so could result in the demolition of the entire planet, all so she could "get what I want." It's worse in hindsight - she abandoned Naota like Amarao when she thought she had successfully extracted his power into Canti, and only returned when it became obvious that this wasn't the case.
Nightmare Fuel: The scene with the (fake) Kamon corpse. "Sometimes you're the cat, sometimes you're the mouse."
Superlative Dubbing: Many Western otaku who are otherwise skeptical or outright hostile towards the dubbing of Animelove the dubbing of FLCL. The series was thought by many otaku to be un-dubbable due to its use of Japanese puns and pop culture references. Synch-Point, the American dubbers, instead replaced those instances with comparable English puns and cultural references. As for the voice actors, the original director of the series supposedly hand-picked the English-language voice actors himself, because it was vitally important to him that they have the same "essence" as the Japanese actors. He was particularly impressed by Haruko's voice actress, Kari Wahlgren.
This Is Your Premise on Drugs: The show does have its share of batshit insanity. And like a drug trip, you can find some nuggets of true brilliance while your housekeeper with a chainsaw engine powered guitar and robot that popped out of your head join you magic adventures.
Toy Ship: Naota and Ninamori. At the very end, it's implied that they'll probably get together eventually if not almost immediately. It helps that it's definitely the healthiest male-female relationship on the show, and Ninamori herself always had the most sincere affection for Naota. In a Ship Tease, Ninamori rigs the play just so she and Naota get certain parts. Also the fact that she unashamedly reveals this to Naota while holding his hand.
Visual Effects of Awesome: The manga sequences in episodes 1 and 6. They better damn well be, since they both took massive chunks out of the show's budget.
Woolseyism: A significant portion of the dialogue had to be replaced for the English version, since the jokes would only make sense in Japanese, and they were replaced by comparable Western jokes and references. One example is the mention of Crystal Pepsi. In the Japanese version this was "Cherio Pop", a gimmicky Japanese soda that similarly sold terribly.
Probably unintentional, but when the show first aired on Adult Swim back in 2003 this was around the same time that AS was airing Lupin The3rd and Cartoon Network was airing Hamtaro. Airing Lupin around the same time really helped newer otaku of the day understand FLC Ls own Lupin references, and the Hamtaro Shout-Out was a nice touch for those who watched anime on both AS and Toonami at the time (yes, Hamtaro was on Toonami at one point, Tom himself lampshaded the strangeness of it's inclusion on a dominantly action-oriented block).