These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: Ansatsu Kyoushitsu
Complete Monster: Takaoka. Not only was he willing to beat up any unruly students, but once they oust him he opts to steal the money meant to be used for the assassinations in order to buy a biological weapon and hire a bunch of hitmen. The virus will eventually cause those infected to be covered in horrific tumors and suffocate. He'd also planned to take Kayno and Nagisa hostage. He was planning on burrying Kayano along with Koro-sensei in a bathtub full of cement and anti-Koro sensei materials in order to force him to sacrifice himself to save her, and take his revenge on Nagisa. He also destroys the antidote during his rematch with Nagisa. Fortunately, Gastro, Smog and Grip are Punch Clock Villains with standards, and Smog never poisoned them with a dangerous poison to begin with.
Ensemble Darkhorse: Karma is a very popular student among the fandom, besides Nagisa. It helps that he's so badass, and not a complete jerk.
Karasuma is also very popular, due to being nice and badass.
Fan-Preferred Couple: For slash, the most popular couple is Nagisa/Karma. For hetero pairing, we have:
God-Mode Sue: Averted with Koro-sensei. Yes, he is an extremely powerful life being, but he has a lot of weaknesses, his personality has many flaws, he was even almost killed in the third chapter, and Karma succeeds to injure him in the fourth. There are often situations where he is the Butt Monkey of jokes. He helps his students to kill him, but he never makes it easy for them, but they are close to kill him. Whenever there are conflicts, he helps his students, but they are the ones who finally solve them, because they are supposed to solve their problems by their own. Koro-sensei is not completely invincible, his students have to save him during the Pool arc. And even his Ultimate Defense Form is a weakness for him because he's immobile in this form, so he suffers from Deus Exit Machina during the Assassination Island arc, and no, there isn't any Deus ex Machina. And even as a teacher, he is not perfect, as the students are not able to pass through the first exams like he wanted. Not to mention that he is inferior to the chairman.
Les Yay: Kataoka saving Kayano in the pool. The latter even says that Kataoka was so cool she think she might have fallen for her.
Kayano makes a similar comment to Yada again.
Magnificent Bastard The school Chairman, who deliberately created a system that would degrade and humiliate a small group of students for the sake of ensuring that everyone else does well. When he realizes that Class E is about to prove themselves, he out-and-out cheats by making it so that the rest of the school had an overwhelming advantage against Class E. That is, his personally teaching the subject matter of the tests, which was changed at the last minute to ensure the preservation of his damn system. All with a smug smile on his face. He even states that maintaining his system is more important than saving the world. Seriously, THE GUY IS A TOOL ON STEROIDS!
Oh, and chapter 23 shows that the system even allows students not in Class E to get away with literally assaulting and battering a student from Class E. He also has the gall to casually drive up to the victimized student and hand him a handkerchief with a smile on his face, and let the bullies go on their merry way scott-free.
Then in Chapter 35 when Class E has a chance of winning a baseball game, he comes onto the field and BRAINWASHES the good baseball team to be more aggressive just to keep up his system. Good lord, this system is life or death to him.
His Magnificent Bastardy is even extending to their training, with him introducing Takaoka Akira into the class. And approving a nightmarish schedule of training, which just happens to not leave them any time to study.
Only for the Chairman to later pull Takaoka out of the class, just to remind everyone else who was really in charge at the school. He wasn't about to let the students or Karasuma have the satisfaction of getting rid of Takaoka themselves, after all.
Moe: After Koro-sensei's upgrades, Ritsu's moe level went through the roof.
Viewer Gender Confusion: Some fans are unsure as to whether Nagisa is actually a guy. His Anime Hair making it look like he has pigtails doesn't help. To make things worse, in the vomic his voice is clearly that of a female.
It gets lampshaded in chapter 43, when they go swimming and a few girls note that it was really hard to tell until that point.