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.
Kumiko Kotoura. A huge Jerkass to her own daughter by disowning her for unknowingly revealing her affair and considered to send her to the mental ward, however she lives in constant regret of the aforementioned disowning and failure to be a proper mother. There's also the fact that her husband refused to help with Haruka, put all the responsibility of 'fixing' her on her, and started not coming home. This combined with the Haruka problem drove Kumiko to drink and have the above mentioned affair. We all know how that turned out...
In the first chapter of manga, apparently Manabe sees Haruka as this as well, and he would like to cross the "jerkass" off from this trope.
Memetic Badass: Manabe, as of the end of episode 2. A later episode where he beats up four grown men before losing the fight doesn't hurt.
COMEDY!Explanation The anime was marketed as aRomantic Comedy. Viewers were first whamed by the Downer Beginning, and after that, the manga spoilers that started to circulate. Rom Com elements still exist in this series, but it's just half what this story was about.
MOTHER OF THE YEARExplanation The Downer Beginning started it, but some translated manga has cemented her status. A similar meme exists for the father and even Hiyori Moritani, Manabe's childhood friend. A Sincerity Mode version also exists for Manabe, mainly due to the fact he's one of the rare decisive anime boyfriends in the past few years.
The ride never ends!Explanation (Spoilers warning!) Some people might be fooled into thinking that after the Downer Beginning or even episode 2, the anime becomes a pure Rom Com. Simply put, it never does. The line itself is taken from a RollerCoaster Tycoon meme (Mr. Bones Wild Ride).
Kotoura-san has 12 seasons.Explanation A mainly Chinese meme. Because of the Cerebus Rollercoaster / Mood Whiplash nature of this work, viewers find what they had every episode can be as much as a whole season in other shows; so they often call "episode X" as "season X".
Moral Event Horizon: The manga revealed Haruka's mother planned to send Haruka to the mental ward and got into a fight with Zenzou about it.
Haruka's parents, due to their (mis)treatment of Haruka— her father is plain Parental Neglect, and while her mother does care for her a bit, she finally disowned her.
Hiyori for Mind Raping and bullying Haruka in episode 2, and made her fell into Heroic BSOD in episode 3. To put into perspective, Hiyori is a Childhood Friend-turned-Hopeless Suitor, a type that can usually get some sympathy from the viewers. However, after the events in Episode 2, Hiyori gets some palatable Character Development that pushes her into being something more tolerable.
Likewise, Manabe, for a short time at least, treats Hiyori with hilarious contempt once her friendship with Haruka is solidified.
The Woobie: It's hard to not see Haruka as one. To quote what a manga-only line when Manabe explains why he found he couldn't ignore her:note It's supposed to be at the second half of episode 1, after Manabe entered Haruka's apartment.
Manabe: *But, to me, she is forcing herself to build a wall around herself with that emotionless face...*
Values Dissonance: Part of the drama of the series comes with the fact Haruka doesn't (and can't) use Tatemae for keeping her (and others) secrets for herself, due of her Mind-reading powers and being the Tatemae an important part of the Japanese culture, it's no wonder why she's rejected by her peers.