Badass Decay: Rio in the anime, after in fact, because of her very badass introduction, becomes anIll Girl but never goes back to her initial level of badassery even after she's discharged from hospital.
Base-Breaking Character: Half the fandom finds Hiyono annoying, the other half think she's one of the best characters ever made.
The Author's free use of "God", "Devil" and even "the Creator", to describe Kiyotaka and Yaiba and the reverence tone they use when refer to them, as if they really are God is especially ridiculous, more because this is a detective manga.
Likewise the Adam/Eve comparison. Yaiba was naturally born with a missing rib and was considered Adam. K Iyotaka was born 16 years later and kill Yaiba, so he's Eve?
Tear Jerker: There are lots of them, especially by the last three books of the manga (Kanone and Hizumi are good at these). Also Charlotte's backstory in Alive.
Wangst: Everything Ayumu says about how he can never compare to Kiyotaka, how there's no hope in ever surpassing him though there's a reason for it, considering what Kiyotaka is,and how destiny always wins because Kiyotaka says so.
Iron and Stoic Woobie (Eyes Rutherford. Despite all the mess that just keeps happening to him, from being cursed to having his best friend turn on him and try to kill him and then dying, he's just not going to stop hoping, and cries all of one single tear in both the anime and the manga. Ayumu as well ; though he angsts a lot in the beginning, he gets pretty awesome at overcoming it all by the end of the manga.)
Ayumu refuses to let himself die, even after all the quite harrowing events of later chapters. He's more or less using this to guilt-trip the rest of the Blade Children to stop moping, live their lives, and Screw Destiny. The way it works out makes him into more of a Messianic Archetype.