Usaida, after the anime started. While some people find him a rather funny character, others are very put-off by the way he keeps letting kids get out of his sight and them leaving the daycare by themselves so easily, as well as the fact he seems to be sleeping in his work all the time.
Of all the babies, Taka is the most iffy. His acting up, constant loudness, and refusal to listen to Kamitani makes him the least liked of the babies, especially since most of them are more well behaved by comparison. However, some aren't too bothered by his behavior since having a more realistically bratty kid in the cast keeps the story from getting too saccharine.
Ensemble Darkhorse: Saikawa isn't actually featured that much in the storyline, since the Manga focuses more on Ryuu's activities at school, but he gets a lot of attention from the fans whenever he does show up.
Fan-Preferred Couple: Between Inomata and Yuki's competition to be with Ryuuichi, a considerable amount of fans are cheering for the winner to be Kamitani. Similarly, Inomata/Yuki has quite a bit of fans.
Fanfic Fuel: Chapter 84 narrates a dream of Usaida's in which all children and teens have their ages swapped; Ryuuichi, Hayato, Nezu, Inomata, Yuki and Yagi are toddlers and Saikawa is the baby, while Takuma, Kazuma, Taka, Koutaro and Kirin are in middle school while Midori is a teacher. Combined with the endcards of the anime revealing their age swapped appearances, works about it aren't uncommon.
Even after realizing that the girl he fell for is Ryuuichi, Inui still gets easily flustered looking at him, especially when he sees him wearing an apron shirtless, a reaction that mirrors Yuki's (who is confirmed to have a crush on him).
When Ryuuichi disguises himself as a girl, Kamitani quickly puts himself in the role of his boyfriend to get Inui away.
Following that, when Inui is close to find out that the girl he likes is Ryuuichi, Kamitani threatens to send Inui flying if he hits Ryuuichi when he finds out.
Yuki is actually jealous of Kamitani for being able to roll up Ryuuichi's sleeves.
The first time we see Ryuuichi genuinely angry, it's not because of anything related to Kotarou. Rather, it's when he sees how Hebihara-sensei, Kamitani's father treated Kamitani.
Les Yay: Quite a bit between Inomata and Yuki as they become closer friends. Yuki is quite prone to remarking Inomata cuteness and call her a pet name Maria-chan.
Misaimed Fandom: Yagi's hatedom largely comes from the fact that they believe him to be a pedophile and the story passing it off as a joke, however, the joke in the manga is the fact that he is always being mistaken by one or accused of being one, rather than actually being one. This is another reason why his scrappiness comes mostly from anime fans, as the manga has delved in his backstory and the reason why he's so fond of children (Nezu and his baby brothers were the ones to keep him company when his parents couldn't be on his birthday when he was really young) and several characters have stated that he isn't one, just a weirdo, but deep down a Nice Guy.
Most Wonderful Sound: A lot of what the babies say becomes this, since the voice acting makes them look absolutely adorable.
Kotarou saying "Nii-cha" often is this. Similerly, him saying "A~gatou" (because he can't pronounce "arigatou") in episode 5.
Nightmare Fuel: Whenever a kid gets lost, expect yourself and the series to start filling itself with Adult Fear. The very idea of a toddler alone in a public place can shake someone who has already had to take care of one to their core.
Toy Ship: As about half of the series focuses on the interactions between the toddlers, this is probably inevitable. Most common ships are Kotaro/Kirin, Kotaro/Taka, or Taka/Kirin.
The Scrappy: A large number of people find Yagi's behaviour towards the children off-putting. This opinion is greatest within the anime-only community but there are a few who read the manga and still find the character genuinely creepy.
Ship Mates: Hayato/Ryuuichi shippers will also often ship Inomata with Yuki, solving all tensions in the possible relationships.
Hayato constantly hits his baby brother Taka when he acts up. This is meant to be Played for Laughs, but Western viewers may not find the act to be at all humorous, even when (or especially when) it's depicted as harmless. This could be attributed to the more lenient attitudes toward family discipline in Japan, where striking one's child is generally frowned upon, but not considered grounds to call Child Services except in extreme cases. This is made considerably worse when Taka smacks his younger cousin Tsumugi for breaking his prized toy sword, when Taka only wanted to be a good older brother in his own right. This is further muddied by Hayato also hitting Kirin at one point - hitting his kid brother is bad enough, but a little girl not even related to him is a big no-no.
Western fans tend to be put off by how often Usaida lets the kids go off by themselves unsupervised; though they probably have a point considering how young the kids are, this still reflects how in Japan parents are more willing to let their children go places unsupervised than in most western countries (particularly in the United States).