Fujiwara. Because of the frequency and perfect timing of her Spanner in the Works moments, a popular fan theory is that she is secretly aware of everything, and is trolling as well as manipulating both of the main characters for her own entertainment. This gets a nod in Chapter 43, where a ramen connoisseur over-analyzes Fujiwara's ramen eating technique and concludes that she's an expert like him, when she was just really hungry and wanted to eat ramen.
A group of fans actually think that Fujiwara's a Stepford Smiler or secretly depressed, given her more heartfelt moments to Kaguya have her mention not wanting to be left out or left to the wayside, her knowing that Kaguya looks down on her, and her piano hobby being all but dropped for mysterious reasons.
Was Ishigami's desire to not tell Ootomo about Ogino's slimy personality born out of true altruism, or just him looking for self-gratification? On the one hand, revealing that would just do a lot of unnecessary harm to her, and the whole point was that Ishigami wanted to help protect her from the shadows. On the other hand, not telling her didn't really solve anything and she remains ignorant and vulnerable to future slimy people, and Ishigami prolonged his suspension and partly caused his own suffering because he didn't want to kowtow to a lie he didn't agree with, which is ultimately validated when the Student Council (and Miko) have his back.
Kashiwagi. Is she genuinely oblivious of Maki's crush on her boyfriend? Or does she know about it and purposely flaunting off their relationship?
Kaguya herself gets some folks splitting ends. While there is a part of the audience that doesn't like her extreme trust issues, her insecurities, and the fact that she hasn't done anything big for Shirogane like the Fireworks chaptersnote and that's if you don't count Shirogane's birthday arc, others like the Character Development she's given (being a Defrosting Ice Queen that's more open to her friends) and her character interactions.
Kashiwagi as she continues dating her boyfriend. As the months go on, she shows that she has major insecurities throughout the whole thing, and some felt like the relationship was very one sided given her boyfriend does all of the big romantic gestures while she just reciprocates. However, her Straight Man role is appreciated, and some do like that she turned out not to be the one played straight character in the series.
Iino, after her initial introduction. A lot of the focus she gets relegates her to Ishigami's former role of being terrified of Kaguya, or her Running Gag of coming in at the worst possible times. While there are some who like those gags and find it a safe basis for her growing role in the council (not unlike how Ishigami or Fujiwara grew), others find it unnecessary because all of her appearances boil down to those two jokes, leaving out her much more interesting characterization during the Election arc. Her gullible and straitlaced personality also splits fans about her, finding her gimmick cute and sympathetic because she tries hard or annoying because she's being mean (especially to Ishigami), and her heavy Ship Tease with him is called into question. She became more accepted as time went on, however, as her initial jokes waned and she was given more quirks and character focus.
As the two leads became more honest with themselves regarding their feelings for one another, the series' main pull became less them trying to get the other to confess and more them awkwardly dancing around their feelings. There are still chapters here and there where they try to get the upper hand, but to some readers they cite the series' tone change as devolving into yet-another-romcom.
Kaguya herself gets most of this criticism. She is still a schemer deep down and will do anything to help Shirogane if she can help it, but after "I Can't Hear the Fireworks" she's become more and more visibly smitten with him while Shirogane can at least hold his feelings in. Some fans cite that as a sign of Kaguya's eventual "defeat", and are upset that her more dominant personality is dormant. She at least develops a routine to prevent herself from overreacting to every little thing, so she's been able to take back some power.
This starts to happen to Shirogane, albeit in a different way, as he constantly tries to take on skills that he's so bad at that it causes Fujiwara trauma as she trains him. Ironically, he becomes good or, at least, decent in these skills after this train.
Chapter 65 has Fujiwara return to her roots as the relatively sane character of the main cast, calling out Shirogane and Ishigami on getting overexcited for elections.
After kissing Shirogane in response to his confession at the cultural festival and falling into a love-induced coma because of it, Kaguya wakes up as her original cold, calculating personality in Chapter 141.
Crack Ship: Ishigami and Hayasaka are a popular ship despite the fact they have only interacted once in the first 50 chapters and that was a single line of dialogue. Mostly due to the fact they are good friends to Shirogane and Kaguya respectively, have similar personalities and both are very popular.
Ai Hayasaka: She has many fans due to her attractive character design, being a top Deadpan Snarker, chapter 59 revealing she's a bit of a geek, and being like a sister to Kaguya.
Kobachi Osaragi quickly gained a lot of fan approval after Chapter 85 which showed her as one of the only people outside the student council who doesn't ostracize Ishigami due to the rumors about him because she witnessed him being secretly kind to Iino, even though he and the latter can't stand each other. She even checked on him without prompting, quietly wishing his efforts to break out of his shell well. Her Deadpan Snarker and not-entirely Covert Pervert tendencies revealed in chapter 80 had already made her fairly popular as Iino's Hayasaka equivalent, but chapter 85 was what really cemented it.
Shirogane's dad started to grown on fans with his hilariously awkward personality in chapter 83. This only grew when he trolled Kaguya into revealing her deepest feelings for his son in chapter 86. And then when it was discovered that his voice actor in the anime is Takehito Koyasu (Dio Brando), his popularity skyrocketed.
Epileptic Trees: In Japan, some fans have pieced together which developments might happen in the series based on the Theme Naming of all the important characters referencing The Tale of the Bamboo Cutter. Mostly, they argue that the final student Council Member will be Kazune Abenote he was on the score ranking, due to his name also referencing Kaguya-hime's suitors; that Kaguya might have an arranged marriage arc with Maki's brother Mikadonote given that his name references the emperor who tried to marry Kaguya-hime; and that Fujiwara will be acquainted (if not given a love interest) with one of the Shuuchin VIPsnote the Saha club President is a second prince from a fictional country, and Fujiwara's namesake is a second prince with his task referencing a fictional country (Hourai).
Ishigami's most popular ship is with Hayasaka due to similar personalities and being good friends to Kaguya and Shirogane. But Fujiwara and Iino are popular with him as well. The former due to his tendency of stopping her and their completely opposite personalities, and the fact that he respects the latter's determination despite her own hangups. In the later chapters, both Iino's friend Osaragi and Kashiwagi's friend Maki have been added to the list of potential partners as well.
A lot of people ship the (currently unnamed) captain of the kendo club and Momo Ryuju, the president of the astronomy club for the Dating Catwoman story potential (their fathers are the superintendent general of the metropolitan police and the boss of the local yakuza respectively). Note that since their first appearance in chapter 39, neither of them had a single line of dialogue until Momo's name introduction and first speaking role in chapter 116.
Friendly Fandoms: The series seems to share many readers with Tomo-chan Is a Girl!, with many people even labeling Fujiwara as "Cotton Candy 2.0" if the above theory is to be believed. Likewise, some have also favorably compared Kaguya's maid Hayasaka to Misuzu.
Growing the Beard: While the series was decently regarded beforehand, many readers started flocking to it during the "I Can't Hear the Fireworks" chapters. But the bigger unexpected moment comes from the author decided to include an ensemble cast that becomes interesting on their own to fill up the rom-com elements.
Heartwarming in Hindsight: When Kaguya is pleading with God to let her reach the fireworks festival in time during the summer arc, she refers to Ishigami as "the first junior I ever had to look after". It's a sweet sentiment at the time since it was the first time she had ever really viewed him in a positive light, but it becomes so much more meaningful in retrospect given how close the two would grow to be over the next 40 or so chapters.
When she was first mentioned, many readers thought that Kei had a crush on her older brother and would be competing with Kaguya for his affection. Then it turned out that not only was she not in love with him (romantically, anyways), she specifically goes out of her way to make sure that nobody ever thinks that she does.
When Shirogane is trying to gauge his likability in chapter 114, Miko says that his face isn't her type and that she'd prefer someone who looked like Sho Hirano. Three guesses who was cast as Shirogane in the live-action movie, and the first two don't count.
Launcher of a Thousand Ships: Ishigami has been shipped with quite a few girls over the course of the series (Hayasaka, Miko, Tsubame, Maki, Osaragi, Onodera, Karen). Fans have been known to joke that he's secretly the protagonist for a harem manga.
Mind Game Ship: Kaguya and Shirogane's relationship in a nutshell. They spend their time messing with each other in hopes of forcing a Love Confession because they're too prideful to give one themselves.
What Do You Mean, It's Not for Kids?: The series is actually serialized in a Seinen magazine, but a lot of readers mistake it for a Shonen series. It's not hard to see why though, as despite being Seinen, there's nothing in it that makes it unsuitable for teenage audience (and is marketed as such in the official English translation). The backstories of the main cast can be quite sad, but nothing too dark and the manga never uses any explicit fanservice elements. This is to a point deliberate. The mangaka has said that he prefers his work to be as widely-read as possible, and is occasionally critical of manga magazines' strict demographic lines in general. This is even mocked In-Universe where the male characters read a manga that is suspiciously similar to the actual manga itself and Ishigami complains about the lack of fanservice.