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.
Base Breaker: Both Kyouko and Sakurako due to being very obnoxious and selfish, acting stupid and stealing the spotlights of seasons one and two respectively. Chinatsu is also this for her Bitch in Sheep's Clothing-ness.
Broken Base: Fandom opinion is split over which season of the anime is superior. Fans of the first particularly dislike the decreased focus Kyouko has in the second, as well as the increased focus on the first year students. Fans of the second season find this refreshing and find the humor to be higher quality.
Foe Yay: Between Kyouko and Ayano. Also, Himawari and Sakurako.
Fridge Logic: So, why did Kyouko smell Ayano's shoes, again?
She smelled them because they smelled like mint, and she knew that because she smelled them!
Internet Backdraft - Among Yuri Fans there have arguments/concerns/disapproval over the fact the Yuri is subtextual instead of being open. Normally a Moe Slice of Life with Les Yay overtones such as this wouldn't get such scorn. The problem/concern stems from the fact it's serialized in a Yuri Hime S, has yuri in its title and is the series with the least amount of Yuri in the magazine, is supposedly the best seller in the magazine - prompting discussions about exactly what Otaku want in their Yuri - and it's the one out of the magazine to get a anime. Considering the fact it's serialized in a Yuri magazine some people would expect characters who are openly lesbian or at least start falling in love with each other, and more actual Yuri but no...
Ultimately the one thing that this show differs from all other Schoolgirl Series is that all the girls are actually stated to be lesbians instead of heavily, heavily implied.
The Yuri Yuri spin-off actually does depict girls falling in love with girls, but it's basically an extra to the main series with different characters, and consequently hasn't been covered by the anime.
Les Yay: What did you expect from a show named Yuru-Yuri?
The first episode has an in-universe example for Kyouko when she goes into Akane's room. The music sounds like something out of a horror movie and she is noticeably shaken by the things she sees inside.
Ship-to-Ship Combat: Any pairing vs. any pairing. With so many overtones and so many pairings, this is expected, even in the yuri community.
Ship Mates: That's not to say there aren't any pairings that get along. Almost everyone ships Sakurako and Himawari, so to go with this pairing you can have the "Friendship Pairings" where everyone ends up with the person they are closest to, this one ends in the most pairings. Then there is the "Sexual Tension Pairings where those that have expressed interest for another character, end up with said object of affection. Sakurako and Himawari, of course, manages to be in both pairing types.
Tear Jerker: Episode 3 of the second season while Sakurako watches Himawari helps Chinatsu make a scarf for Yui. The music doesn't help.
The eleventh episode of the second season in which Akari is deciding on whether or not to change the past and face the consequences of losing her old memories in the place of new ones.
Mirakurun's Heroic Sacrifice in the season one finale. Though she is back again in season two.
Yandere: Akane, only in the fandom. There are many Pixiv fanarts featuring her in this state over Chinatsu raping/making love with her sister Akari. Ironically, Chinatsu has some (canon) yandere tendencies as well.