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.
The whole thing is similar to the Broken Base of Neon Genesis Evangelion regarding Yukiteru and Yuno. Some fans think their English voices are terrible and don't fit their characters, other fans think that not only does the English voices perfectly fit their characters but also makes it a refreshing change of pace from the high-pitched girly voice and shy, insecure, young boy voice that have been overused a lot in anime.
Yomotsu Hirasaka, though that's kind of inevitable for a blind insane Super Sentai parody.
Crosses the Line Twice: Takao Hiyama appears in a flashback in the middle of one chapter... only to take a spear in the back, courtesy of Yuno. Him being an Asshole Victim is probably what makes it so funny in the first place.
Draco in Leather Pants: The more avid fans of Yuno tend to tone down her more negative and violent qualities in favor of her devotion to Yuki.
Die for Our Ship: Both Yuno and Akise are victims of this, though the latter has it more prominently within the fandom. Notably, it actually is in-character for Yuno to kill people that come between her and Yukkiteru, though it's more often this trope than Murder the Hypotenuse.
Yukiteru and Yuno betraying and slaughtering the 8th's orphanage.
Yuno crosses it when she lies to Yuki and convinces him to kill his friends, all of whom were only trying to help him; she even delivers an Evil Laugh when she learns about Yuki shooting Hinata. Of course to somefans, this might also be the moment that solidifies how awesome she is.
Yuki also crosses the line here, even if he was being manipulated.
Tsubaki crosses this when she orders her followers to strip off Yuno's clothing... and to gang-rape her, all so she could lure Yukki out of his hiding place.
Mur Mur crosses this when she undoes the positive future in Paradox by deliberately erases everyone's memories and goes back in time to make sure that the 2nd is still alive and kills them all. She also uses the wounded Yuki to prevent Akise from stopping her plans.
Akise in the manga crossed it when he abandons Yuki's friends to let them die by Yuki's hands, just so he can get the chance to kill Yuno. Even Yuki is disgusted by this. Defied in the anime, where he actually tries to stop Yuki.
Rooting for the Empire: Plenty of fans were rooting for some of the other Diary Holders (like Minene or Yuno) to win instead of Yuki, seeing as how they came off as more sympathetic and likable.
The Scrappy: Yukiteru gets the most heat out of the entire cast, despite being the main character.
His father Kurou isn't any better. At first he seemed like a Handsome Lech who was still a good father, however, he soon reveals to a Dirty Coward who wanted to dispel his money troubles by destroying his son's phone note though to be fair he didn't know it would kill him. He crosses the Moral Event Horizon by abandoning his son to die on the collapsing tower and then stabs his wife when he calls him out for it.