Miu, many fans were not happy with the reveal that after the Miu rescue arc, Miu was once again a much stronger fighter than Kenichi. This then led to arguments about when Kenichi should become better than Miu or if he should at all. She's also the poster-girl for the amount of backlash this manga receives for its "unnecessary" fan-service as described in Broken Base.
The fan-service. You either find it enjoyable to a certain degree, or it's an unnecessary distraction to those who are reading for the fights and storytelling. It just gets much more blatant, and in-your-face, as the series goes on; further alienating the detractors. The worst of it being the manyweird- angleshots of a helpless Miu seen throughout the Amusement Park arc during what is supposed to be an intense fight between Ogata and Tanaka.
The ending as to, whether or not, it was too abrupt of a closure. The fact Yami still has several prominent members at large doesn't help either.
Cargo Ship - Kii Kagerou x Setsunamaru (his sword). Completely canon; when he is forced to use another, he apologizes aloud for cheating on her. He also frequently calls her "beloved". It's even reciprocated.
Siegfried's first love was a violin.
Complete Monster: YAMI Master Silcardo Jenazad couldn't stand lasting peace, so 20 years ago he incited a civil war, which he's still actively maintaining, in his own country. During said civil war, one of Jenazad's servants informs him that the men, who joined his side, because they were devoted to his cause, will die in large numbers if they persist in the current segment of the conflict. Jenazad's response: "So?" For his research purposes, Jenazad causes his past students to fight and kill each other. He causes an avalanche to try to kill his own modern-day YOMI student. Jenazad also almost manages to trick fellow YAMI member Akira Hongo into killing the titular protagonist, and kidnaps and brainwashes Furinji Miu into becoming his newest cold-blooded disciple. He later supervises the brainwashed Miu's battle against Kenichi, with the expressed purpose of getting her to kill Kenichi, following which her mental state will be completely subject to Jenazad's manipulation and the brainwashing process to convert her into his thinking will be complete. Jenazad detests peace so much he is willing to kill his country's deposed princess (the sister of the aforementioned "dead" YOMI disciple), who is all for restoring peace to the nation.
Crazy Awesome - All of the masters are crazy and awesome to various degrees. Siegfried, the guy who spins around like a top and sings while pounding his opponents into dust also deserves a mention.
Shigure gets a crowning moment of Crazy Awesome in chapter 285. She and Kenichi are ambushed by three skilled assassins after Shigure's head. She takes out all three of them (two of them with her hair ribbon) and left all three alive. Awesome enough. What puts this in Crazy Awesome territory is that she does all this while completely naked. Also randomly decides to terrify waitresses with shurikens and thrashes delinquents with spoons.
Over the course of their two battles, Akisame Kotetsuji and Alexander Gaidar attack one another with sculptures made from steel rebar, carve statues out of rubble and generally turn whatever place they're fighting in into an art museum.
Siegfried also counts.
Ensemble Darkhorse: Renka, despite not appearing very much till about chapter 310, is incredibly popular.
Foe Yay: Some people claim this is the case between Sakaki and his Rival the God Fist. After seeing this page, they may be on to something. Although they were just kicking the two people behind the other.
Both of Renka's fights against Rachel. In the amusement park, they end up wrestling each other stark naked. Also, Rachel didn't strip them for attention, since there was no one there.
Germans Love David Hasselhoff: If Wikipedia is any indication or the number of memes and Facebook groups, then it's safe to say Kenichi is BIG in Spanish-speaking countries!
Nightmare Fuel: The end of Chapter 524. Ogata crushes Tanaka's head with an elbow strike.
Hayato Furinji is the most powerful member of the Katsujinken side. Oganosuke Yogi, the leader of YAMI's armed division, is his match in every way. There's someone on the side of the badguys as powerful as the Invincible Superman. Think about that.
They Wasted a Perfectly Good Character: The entire Hachiou Executioner Blade team. They were built up as equals to the the top Yami masters, but are treated as little more than an ineffective Quirky Miniboss Squad. They have their own band of weapon-wielding disciples in Yomi for the Shinpaku Alliance to fight, only two even have names so far, but aren't as wasted in comparison because they ARE just a Quirky Mini Boss Squad, and are close to overwhelming the Shinpaku Alliance. Time will tell how effective they remain after Yomi-Unarmed's collective Heel–Face Turn.
And with the manga having ended, any expectations for further development for the squad (as well as any other characters) is gone.