Alternate Character Interpretation: Zenkichi. A person only motivated by a Subordinate Excuse and following Medaka's justice, or a truly heroic character who simply gets stressed with the burden of helping people? Or both? In canon, he seems to think it's the first. Though he was going through a bout of self-deprecation at the time.
The fighting-manga arc has been going on pretty much nonstop since the series came close to being canceled. They stopped for a single chapter, if only for exposition to introduce the new set of villains, then jumped right back in.
The Successor arc, while providing nice deconstructions to shounen manga, still wasn't as eventful as the other arcs despite its length, and much of its content felt random and disorganized. Medaka's characterization didn't help its reception.
Ass Pull: Lots. Especially with combat — not that it was handled badly. That is, until Naze Youka being Medaka's never-mentioned-before older sister Kujira. There are hints (her eyes being the same as Medaka's and Maguro's being the main one) but only subtle ones, and it still feels like a huge stretch.
Base-Breaking Character: Medaka is either a deconstruction of The Ace or played overly too straight despite the many attempts to show her faults. She became more controversial when she Took a Level in Jerkass toward Zenkichi during the Successor Arc. Losing her position to Zenkichi and becoming a "regular" student brought her down a peg and made her more likable and entertaining.
Broken Base: Regarding the various Genre-Shifts; some people preferred the slice-of-life elements of the first arcs, some preferred the straight up battle manga, and some prefer the Deconstruction manga.
Crossover Ship: Kumagawa would find a kindred spirit in Nagito Komeda from Danganronpa due to their similar views on life and self loathing. Thanks to Kumagawa's power, he is one of the only people Nagito needn't worry about accidentally killing with his luck.
Clueless Aesop: This trope has fans all over the internet scratching their heads behind the true meaning of Medaka Box. Is it a Satire, or a parody of shounen? What is the author's stance on shounen anime? Was it all simply a deconstruction that's been reconstructed? Or was the author even serious about the series at all and is just writing things in at random? Seriously, WHAT WAS THE AUTHOR THINKING?
Aka Aoki. She's been in three chapters, has barely moved from one spot, and didn't even fight. There is already a whole bunch of fanart of her on pixiv. Probably because she's a nurse though...
Youka Naze and Kei Munakata also count as they consistently place in the top 10 on popularity polls despite not being main characters.
Surprisingly, there is Nienami Namanie, who has had a ridiculously little effect on the plot compared to her overwhelming popularity in the fandom.
Nekomi is popular for her Combat Pragmatist ideology while being perky at the same time. Nekomi is this in-universe as well. As a Special she ranks relatively low on the power scale but is very popular with the student body for her David versus Goliath victories using Combat Pragmatism.
Evil Is Cool: Kumagawa. He starts out as the third Big Bad, and Medaka's Arch Enemy and complete opposite. His dissonant serenity and overall humor arguably make his character more interesting than Medaka's. And having a status change doesn't deter his status in the slightest. In the second Shonen Jump popularity poll contest, Kumagawa won with almost four thousand votes. The second place holder (Medaka) did not even reach one thousand votes. And for a while he was either played as The Dreaded or the Big Bad. His popularity became much higher than even the main character, he's got his own one shot story, and became somewhat of a flagship character for the series. Just compare the amount of fanarts he gets to the rest of the crew on pixiv! Maybe even some people who aren't into Medaka Box know him by now. Much of his success must be related to his Cool Loser and Lovable Sex Maniac traits, also. Gets a lampshade hung on it in chapter 128.
Ajimu: If, for example, this world was a manga where you guys were the main characters, if there was a vote for the favorite character, someone like Kumagawa-kun might unexpectedly come out and take first place.
Fan-Preferred Couple: Zenkichi/Emukae, as well as Medaka/Kumagawa definitely seem to be fairly popular, compared to the canonical affection Zenkichi has for Medaka which seems to be reciprocated as of Chapter 140.
Idiot Plot: You would think that in episode eight, where it demonstrates Onigase's strength, the handcuffs wouldn't be too hard for her to break. At least Medaka had the excuse of "she didn't think Onigase would want the handcuffs broken."
Jerkass Woobie: The true nature of the Minus class. To quote one Minus: "Do you know the taste of gas that your parent makes you swallow? How about the taste of licking a perverted teacher's shoe? The taste of sand that your classmates make you swallow? At least you know the taste of a newspaper that was the only food you could obtain? Of course you don't know, because you guys are the happy ones. But those kinds of tastes are just how it is for us, Class Minus 13's members. We have experienced the worst, that's why we can do the worst."
Hitoyoshi has Medaka, Shiranui, Kikaijima, Mukae, Ajimu, Naze, Akune, Kumagawa, Maguro, Munakata, and now Tsugiha.
Kumagawa is also shaping up to be this, sharing pretty much all of the above characters, but replacing himself with Hitoyoshi, Maguro with Gagamaru, Munakata with Shibushi, and Tsugiha with Ima. And for some reason there was a picture of him and Shiranui with Hinokage...
Magnificent Bastard: Kumagawa Misogi, the primary antagonist of the "Kumagawa Incident Arc," is Dissonant Serenity incarnate and the dark-tongued leader of the Minuses. On a quest to bring the elites down to his level, Kumagawa introduces himself thrashing the members of the Flask Plan with an impenetrable smile on his face, revealing himself to be the one person Medaka Kurokami could not save and the one who manipulated Secretary Akune into indulging his former violent impulses. Unusually good at reading people, Kumagawa worms his way into the student body and creates Class -13 in an attempt to usurp the current Student Council. All throughout the subsequent battles, Kumagawa constructs scenarios that end up neutral at worst or outright benefiting him no matter the outcome. Charmingly enigmatic and ever-equipped at bouncing back, Kumagawa leaves little wonder why the fandom enjoyed his character.
Shiranui seems to be an extremely cute girl with an ahoge, but she has flat out said she enjoys following Zenkichi and the crew around because he keeps getting beaten up, and has tricked him into getting mauled by a giant wolf, as just one example. The look on her face when she refuses Medaka's offer of being vice president is pure Nightmare Fuel.
Medaka can be quite... enthusiastic when improving people. Especially after the Successor arc, she shows no hesitation in wanting to fight Zenkichi without any remorse beforehand. It clearly shows just how unnerving her behavior is.
Several of the faces War God Medaka makes during her Unstoppable Rage against Myouri.
Unzen in general is pretty unsettling due to being a Creepy Child with no problem with killing.
Iihiko tops them all. Managing to scare frickin Anshin'in of all people and taking it a step further by killing her with one hitusing a rubber band. His creepy demonic appearance and his ability to negate everyone else's powers are not helping.
Ron the Death Eater: Medaka seems to be intensely hated by certain segments of the fan-base, people going so far to say that she is far more evil that Kumagawa or Anshin'in and deserves to die/be raped/be mindraped/treated like garbage/etc. for her crimes of wanting to help people note in a matter of duty rather than true empathy and treat her enemies more like friends, thus isolating herself from those who are her real friends. and not showing Zenkichi favoritism.
Tastes Like Diabetes: Medaka, though rarely. Zenkichi noted it as one of her fortes. You can see rather clearly near the end of Episode 6, when she kisses Kikajima in midair.
They Wasted a Perfectly Good Character: Zenkichi and his family. Earlier on, it's implied that Zenkichi himself has abnormal potential, and this is only given more fire when it's revealed his mother is an abnormal. Yet these points (as well as his overall upbringing) are neglected in favor of making him a Satellite Character to Medaka.
True Art Is Angsty: Youka Naze, who gave up a life of luxury as one of the Kurokami children due to the theory that true genius can only come from living through hell. She decides to stop this attitude in exchange for helping her brother save Koga's life.
IF I'M ONLY GOING TO BE HAPPY, I'M BETTER OFF DEAD
True Art Is Incomprehensible: Becomes a plot point with Yabaru in episode 7, who wants to capture the beauty of a goddess, but turns down various girls, and even the guys, until Shiranui shows up. The fact that he chose her to represent what he wanted (potential for growth, as opposed to fully grown figures) doesn't sit well with the girls.