Die for Our Ship: Poor Yuiko. She's constantly bashed and demonised for having a crush on Ritsuka, even though she never acts on these feelings. She even encourages Soubi and Ritsuka's relationship from the beginning (earning a She Is Not My Girlfriend reaction from Ritsuka) and is shown to be friends with Soubi as well, and yet she's still somehow seen to a threat to their relationship.
Draco in Leather Pants: Ritsu, Nisei, and Seimei are the most frequent, despite the manga practically spelling out the fact that the last person is a psychopath. And while not villainous, Soubi is often stripped of his flaws to become a total saint.
Fridge Horror: Seimei and Nisei had split up to attack the school for the Sentouki. While the latter had been in a fight with Ritsuka and Soubi (previously Midori and Ai), Seimei was left to his own agenda. Although he's the Sacrifice of the two, he somehow managed to cause the majority of the problems listed in Crapsack World above. In other words, it may very well have been him who destroyed part of the Old School and injured others. The question is how? with a dose of with what?. It's unknown who injured the unnamed four people, but there was not enough time for Nisei to attack and wound four people by the time he reached Ritsuka, Midori and Ai. He reached them pretty quickly - even before the announcement that there was an intruder. After the fight with Ritsuka and Soubi, he was also unconscious, then taken captive. This goes back to the fact that the only other person who could have done all that damage was Seimei.
It could very well be that the book Seimei recounted so offhandedly in volume 8 was actually a retelling of what happened to Mikado in volume 11.
Related to the universe itself - losing your ears and tail. This troper was watching and then it hit her that new non-virgins must experience some sort of phantom limb syndrome the same as real-life amputees. For people who lose their ears consensually it must not be that bad - but what about those (like Soubi) who were raped? The phantom limb syndrome would only serve as a physical reminder that they were assaulted.
The Slut-Shaming concept in this universe. On the one hand, it'd be hard to slut shame someone who still has their ears (though conversely, poor Shinonome is ridiculed early on for still having hers as an adult, showing that virgin-shaming is a thing as well). On the other hand, anyone without their ears, no matter how they lost them, is now fair game. And the worst types would de-ear the person themselves, whether the person wanted to or not.
Also Soubi's overly-physically-affectionate behavior towards Ritsuka takes on a very unsettling light once his backstory is revealed, since sexual abuse victims, especially those who were abused as children, often engage in inappropriate behavior because they come to think of it as normal.
Jerk Ass Woobie: For some, Misaki. Yes, she treats Ritsuka terribly after Seimei's death, but then again Seimei wasn't the nicest person towards her, and more than one person were on the floor when she got Hidden Depths in volume 5.
Mind Game Ship: Any ship involving Seimei. People who ship him and Ritsuka as a normal couple are known to be part of the Misaimed Fandom, seen below.
Misaimed Fandom: While Seimei was, in fact, first portrayed in a positive light by Ritsuka as a caring older brother who is unfairly murdered, he is shown in later chapters to have faked his own death to avoid his execution. It goes From Bad to Worse when it's revealed that he was going to be executed for being a murderer. And to top it all off, he does all of this just to sadistically test his brother's love for him. While this recieved a Squick reaction from some fans, others loved Seimei even more, making him into, horror of horrors, The Woobie.
Though Ritsuka might seem to be an Unreliable Narrator, the things he described about Seimei were in fact accurate, though only toward him. Seimei did do all those kind, caring things for him, regardless of his actual intentions, regardless of how he acted toward anyone else, etc. Ritsuka was simply describing Seimei exactly from the things he did around Ritsuka himself. It's a bit hard to explain, but he's not entirely unreliable (as Seimei really does only care about him, though not necessarily out of love), though he is a bit the type to only believe what he wants to believe, which Soubi has noticed. In terms of Seimei, some fans do enjoy the complexities of his character and do like him more for not actually being the kind, caring older brother, but for being so different from the rest of the cast, and for being an exceptional villain.
The cute art style and fairly non-explicit relationship between Ritsuka and Soubi leads to a lot of younger fans mistaking it for something sweet and fluffy — often completely missing the point that the series, and in particular Ritsuka and Soubi's relationship, is supposed to be quite disturbing. (After all, Ritsuka is twelve years old, and Soubi is pushing him into a romantic relationship because Ritsuka's own brother told him to.)
Ron the Death Eater: Yuiko is a constant victim of this, to the extreme that one infamous scanlator team kept calling her "stupid", "bitch", "slut" and saying "why don't you kill yourself now" in their foot notes.
Tear Jerker: When Natsuo and Youji are called back to school, and they genuinely don't want to leave Soubi and the others. Even Soubi appeared saddened when he found out. Thankfully, both boys come back to live with him again.
They Wasted a Perfectly Good Plot: The virgins-got-cat-ears thing really could have been used for much more. It would have made for some interesting stories, and it would be fun to see how it affected society. How would it affect teenage sex? How would it affect paedophilia? Would there be an entire market for fake cat ears? The possibilities go on.
Considering the fact that Kouya had fake cat ears she put on around her schoolmates, there probably is a market for it.