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.
Idiot Plot: A mild example — perhaps more of a None-Too-Clever Plot. But it really should be obvious to anyone paying attention that something odd is going on between Aoi and Kaoru; even the way they address each other — Aoi calling the ostensibly lower-caste Kaoru "Kaoru-sama" while Kaoru calls the ostensibly higher-caste Aoi "Aoi-chan" — should make people suspicious. Even more egregiously, while Aoi and Kaoru may have reason to keep their engagement low profile to avoid antagonizing Aoi's family, there's no good reason for Kaoru to pretend he's romantically "available," except that it keeps the "hilarity" going.
Averted in the manga, where, in spite of being sidelined or downplayed for comedic purposes most of the time, it is made fairly clear that Aoi's family is putting extreme pressure on Aoi and Kaoru to avoid giving any sign of being in a relationship. They even go so far as to actively attempt to break them up by trying to get Aoi to marry another man. This persists all the way up to the final volume where Aoi is practically kidnapped in an attempt to get her to marry the other Kaoru who is supposed to be the new heir to Hanabishi clan. It's made clear that Aoi's father has been opposed to her relationship with Kaoru up to the very end. This troper is a little surprised that her father didn't put out a hit on the guy (you know, aside from the fact that that would have comprised the author taking the genre and structure of his story and breaking them over his knee).
Les Yay: Tina likes groping other women's (and girls') breasts. But she's really in love with Kaoru. Also, there's her threat to go kiss Aoi and Miyabi if Kaoru won't kiss her.
Miyabi's life revolves around Aoi, and she admits feeling jealousy toward Kaoru, as well as a belief that he is unworthy of all the effort Aoi has been putting in to prepare for being his wife.
Played with when Tina discovers Aoi's habit of hugging people or objects in her sleep. She tells Aoi the next morning, "I thought I was going to have to switch teams just to survive," and there's an Imagine Spot of a wide-awake, seductively smiling Aoi fondling her. Meanwhile, the real Aoi is going into spasms of embarrassment, complete with Luminescent Blush and Big "NO!".
Moe: Wouldn't really be an Unwanted Harem show without tons of it, right?
Purity Sue: Some viewers / readers see Aoi as this. To an extent, Values Dissonance between Japanese and American cultures.
Tastes Like Diabetes: Some feel this way about the romance between Kaoru and Aoi, especially as the series goes on and on and on.
Tear Jerker: The episode Moonlight. Tina lets everything out to a sleeping Kaoru, since she's leaving tomorrow, and couldn't bear to tell him it's supposed to be for good. She kisses him partway through. He then turns over and mutters Aoi's name. Tina now knows where Kaoru's love lies, though they've been hiding it out of necessity the whole time. Her expression says it all. * sniff* The fact that she's still shown to love them both dearly despite this is Tina's Crowning Moment of Awesome. Still choked up. The manga issues that "follow" the anime just raise the respect meter more.
Tina: "Kaoru ... I have just one favor to ask. Never ever stop loving Landlady-san. A favor for the girl who can never be your girlfriend."
Manga Chapter 43 when Aoi/Santa-san gives Kaoru the dream of seeing his mother again. (I'm ok now.)