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.
Kuroha too in some smaller circles, due to the fact he mostly serves as a plot device and originally wasn't even supposed to be part of the story until he was inserted into an official Music Video. There are also people who get annoyed whenever fans are diehard for him, finding him overrated.
Mary also has her own dedicated following, since her general innocence, shyness, and being The Klutz make her very endearing to fans.
Hibiya has his fans largely due to being an adorable snarker and for having the most iconic song in Kagerou Days.
Fanon Discontinuity: Due to the anime's questionable quality and how it's version of the story worked out, many fans who were in the fandom before the anime aired have chosen to either ignore it's existence, or take it for what it is while not actually considering it part of the canon.
Late-Arrival Spoiler: Haruka and Takane being Konoha and Ene's former selves is considered common knowledge among the fandom. It's also hard to talk about Ayano's importance to the plot without eventually mentioning her being Mekakushi Dan's founder and surrogate older sister to Kido, Seto, and Kano.
Additionally, the fact that Hibiya is listed as a member of the Mekakushi Dan should be a big enough hint as to who survives the Time Loop between him and Hiyori.
Early on in the anime's airing, new fans had gotten upset over being spoiled about certain things such as characters having eye abilities- something that is considered the most basic knowledge among the fandom.
The order in which the music videos were released as well. After Konoha's State of the World, a continuation of Heat Haze Days, Kisaragi Attention was released, which is one of the happiest songs in the series. And following Yuukei Yesterday's release was the Nightmare Fuel-induced Outer Science. Summertime Record was completed two days after.
Chapters 17 and 18 of the manga. In Chapter 17, we're finishing off Takane's route, it's a little bittersweet, but still optimistic. Then at the very end we see Kuroha. In Chapter 18, Kuroha immediately brutally murders Seto, Kido, Kano and Ene on page before Mary resets the route.
Moral Event Horizon: Route XX Shintaro arguably crosses it when he chokes Ene to death when she was just trying to help him.
Kuroha, when he murders everybody.
Nightmare Fuel: Kuroha's expression in the MekakuCity Records crossfade PV.
Outer Science in general.
Everything about Kuroha for that matter.
Mary, screaming silently at the end of Outer Scienceas her hair falls out, forms into snakes and turns black and scales grow over her skin. Seeing the series' most Moe character like that is... just upsetting.
Shintaro, Ene, and Konoha are sometimes shipped like this too due to their canon interpersonal relationships. Also popular is any shipping between the One True ''Foursome'' made up of Shintaro, Ayano, Haruka, and Takane, affectionately known as the "Yuukei Quartet" by fans.
Tear Jerker: Ayano's suicide, and Shintaro's reactions in Toumei Answer and Lost Time Memory.
And then Ayano no Koufuku Riron came along and made it even worse.
Challenge. Watch Yuukei Yesterday and then Outer Science. Or just read the manga up to Haruka's death and try NOT to cry a single time. If you win: good for you. If you lose: congratulations and welcome to everyday life of the fandom
The Kagerou Days time loop, and its affect on Hibiya in Otsukimi Recital.
Mekakucity Actors episode 11. Not only is Shintaro's ability revealed to be the "Recording Eyes" ability, but he's been with it since he was in the womb.
What Could Have Been: Jin stated in an early interview regarding Hibiya's background (before he was properly introduced in the novels) that he would be Childhood Friends with Hiyori. He also mentioned that Hibiya's quite popular in school, his only downfall being that he can't get Hiyori to notice his feelings for her. By the time he's properly introduced in the novels, however, with the exception of his unrequited crush on Hiyori, his background is completely rewritten.
Konoha was originally supposed to be a girl.
Jin originally wanted to name the series Mekakucity Project, which was evident when all of his major KagePro-related albums are called Mekakucity ______. However, Kagerou Daysgot too popular and so Jin was forced to name the series after it. He eventually got his way in the anime.
Well-Intentioned Extremist: Though Ayano obviously always meant well, and everything she did was for the sake of her friends and family, many of those things were... not very well thought out. Such as pulling off her suicide stunt when Kano was right there, and just in general getting him involved in a situation that ultimately made his already poor emotional health even worse. Not to mention Kido and Seto who also suffered from losing her. Ayano was so concerned for her adopted sibling's lives that the emotional impacts her death would have on them apparently slipped her mind.