Base Breaker: Fans either adore Musashi for trying to prevent a bad future while looking awful pretty doing so or can't stand him due to how obnoxious he can be, especially to Yamato.
Broken Base: The amount of Ho Yay / Foe Yay in the series, specifically between Rune and Yamato. Some find it to be a great amount of Squick and unnecessary, and other see it as crucial to the storyline.
Designated Hero: The main character has a bipolar outlook on the good of the world. The "good" characters are very enigmatic and don't seem all that attached to even each other. They also happen to be the world's last hope in being saved from an amoral scientitst's products of destruction. Yep, Stan Lee's bringing in the Marvel touch here.
Fridge Brilliance: Remember, Dunstan created Ultimo and chose Yamato to weild him. His takes on "good" and "evil" are pretty damn twisted, so it's no surprise that Yamato isn't your typical hero.
More like it relies on it. Nothing in the series is expressed through long speeches, they're expressed through Wham Chapters and deeply unexpected plot twists.
They actually do use long speeches, usually to point out The Power of Love or good and such.
Jerkass Woobie: Rune. By now, it's safe to say that he's done more things to garner Squick than sympathy from the fanbase. Especially to Yamato. But in a way, it's justified, as Ultimo did kill his past self.
Murayama Musashi. While his whole world was destroyed, his rude quips to Yamato and tendency to rather recklessly do things himself places him in this territory.
Fridge Brilliance, when you remember how earlier Hana tells the school guard that her teacher told her that she had no parents. This may as well mean that the evil elementary school teacher brainwashed her into becoming the master of an evil doji.
Villain Decay: Is Vice truly the epitome of evil? For more than a year's worth of chapters put together, Vice hasn't been shown doing anything except eat hamburgers and yell at K while just lazily sitting around in their run-down apartment. YMMV if his dynamic entries make up for this.