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: The fandom, not to mention the audience in general, is very very broken. Much of it stems directly from Alternate Character Interpretation, and a great majority of the rest from taking the comic seriously. Of course, the fandom is far from agreeing on whether the comic is lighthearted entertainment, albeit highly dramatic and with dark and difficult themes, or a more serious work, albeit at times comical and unapologetically sprinkled with erotica and fanservice, and how it "should" be read.
On one hand, there is a bunch of fans who love Linneus for being cute, dainty, sweet and a Love Martyr - an ever popular character type among Yaoi fans; on the other hand, you have the ones that can't stand him for being far too effeminate, gutless and weak, even for an Uke, and perhaps stupid for lingering on a love that cannot be fulfilled. Or for just being the cardboard cut-out Gender Flip of your clichéd insecure-teenage-girl-with-no-spine who dreams about Reformed Rakes. Likewise, is Xanthe acting like a major asshole because he is a dick or because he's a thoroughly broken man? Futhermore, should Emirain be "allowed" to have one Uke stereotype character along the ranks of less stereotyped bottoms, or is Linneus' ultra-uke-ness opposable in and of itself?
For that matter, the whole main plot, Xanthe/Linneus, is a major base breaker, much due to the individual character interpretations, but also as and of itself. Run-of-the-mill forbidden love cliche? Or highly complex, tragic situation?
Or the other main couple: Rhys, Troubled, but CuteMagnificent Bastard who one loves to hate or hates to love, or an utterly selfish, inconsiderate Jerk Ass who likes to manipulate underlings into sex and rape straight male prostitutes? Axis, victim-of-circumstances sex slave who's forced fo accepti a moneyed client he does not want, and who beats and rapes him, or a closeted Gayngster who secretly enjoys his volatile one-up-ridden thing with the blue bastard? Word Of God confirms that Axis has the hots for Rhys and doesn't mind having him nearly as much as he lets on.
Yvette also. Many hate her simply for being Xanthe's wife, many for the fact she openly manipulates him, the rest give her the benefit of doubt or at least think she's too childish to be conscious of all the effects of her actions.
Broken Base: Pretty much everything in Teahouse is more or less universally appreciated or at least tolerated by fans. The fandom specifically can be divided in two: those who like or are interested in the Linneus/Xanthe arc, and those who find it boring or love to hate it.
There's also the fact that most of the fanbase will not tolerate any complaints from other fans. If a page is delayed, whether announced or not, you can count on a multitude of comments flooding this same page showing nothing but praise for Emirain and all-around guilt-tripping to anybody who doesn't feel the same way they do. While comments full of vitriol will pop up, they are immediately removed by moderators. But any comment that voices disappointment in a delay, even if said comment is polite, will immediately be flamed and the commenter will be insulted for being "selfish" and/or "childish". There's also the favorite "This comic is free so you have no right to complain" argument.
This is also true when people question the setting or voice concerns about the ethics of the Teahouse. Fans and even moderators will tell them to stop forcing 'real life' standards onto the comic because fantasy stories are allowed to play by the creator's rules, not anyone else's.
Designated Hero: any of the main cast, if you don't like them as characters. And the main cast all have a bunch of personality flaws, so if you want to hate them, it's easy.
Lilith is unpopular to say the least, since she has passage into Xanthe's pants while Linneus is left USTing.
Yvette has only been introduced for a few pages and she's already being flamed for being married to Xanthe, being pregnant with his child, and for using manipulation so her workaholic husband would actually spend time with her. From just a few pages some fans are convinced that she's a manipulative bitch who tricked Xanthe into their marriage/the baby/both, told Linneus about the baby just to hurt him, and since its clearly an arranged marriage Xanthe doesn't have to be faithful to her because she didn't 'earn' him.
Draco in Leather Pants: Xanthe regularly treats everyone around him like dirt (even his childhood friend/romantic interest Linneus), owns a brothel where the staff are essentially slaves (complete with branding), and regularly cheats on his pregnant wife and neglects her (with people who aren't allowed to turn him down). Yet there are countless fans who are willing to defend him.
No one will argue you if you say that Prince Rhys is a fully-fledged bastard. But is he a Magnificent one or an unforgivable one?
For a character who, until page fifty, didn't have a single line of dialogue, Mercutio is wildly popular. Which is hardly surprising, considering who he's named after.
Gilder, who's only appeared in 7 pages so far, seems quite popular.
Heartwarming In Hindsight: Xanthe's adding of two sugar cubes to Linneus' tea made for a very heartwarming scene on its own, but its heartwarming level was upped after a later childhood flashback scene between the two, where Xanthe lightly chastises a young Linneus for putting sugar in his tea at all but then indulges him anyway.
Iron Woobie: Yvette. It's not easy being the lead Seme's wife in a yaoi comic, but she does her best to keep a stiff upper lip. Although how well she understands the situation is up to debate...
Xanthe's wife pops by to greet an old friend, announce an expected pregnancy, and try and talk her husband into spending a little less time away from work. The most rabid parts of the fandom have taken that she, respectively, only continues to pretend to be Linneus' friend to keep him handy for backstabbing, deliberately tried to hurt his feelings with the baby news, and deliberately and coldly manipulates Xanthe.
Remy is not only blamed for Axis flirting with her and teasing Rory, she's also accused of sexually abusing her own brother. The "proof" is Rory not being happy to see her in a brothel, masturbating thinking about her, and headcanon about all of the courtesans choosing to be slaves. She has acted in a stalkish and intimidating manner, especially when she visited her brother in the middle of the night to threaten him, but even a panel of her listening in on Rory has caused dozens of comments of fans wishing her dead.
The Scrappy: while no single character is universally hated, there are some very popular choices:
The majority of the fandom (if the comments are anything to judge by) hates Lilith, because she comes between Atros and Linneus and the fact that she is a gigantic bitch.
Yvette, mostly because she's the biggest obstacle between Xanthe and Linneus, being Xanthe's pregnant wife. Although Yvette isn't quite as universally hated as Lilith.
Linneus himself gets a lot of hate for being a passive, effeminate, sparkly, pink epitome of the uke stereotype.
Remy, Rory's sister, got this the moment Axis started flirting with her and he teased Rory about being the "ugly twin", because apparently that's her fault. Even though she's a maid and is supposed to blend in with the furniture, and that Axis has been a twit towards Rory forever, and doubled the effort after Rory topped him as the big earner of the house.
Uncanny Valley: Linneus sinks into this sometimes. He ends up positively frightening in some pages◊.
Unintentionally Unsympathetic: One of the biggest causes of the Broken Base in the fandom. Despite being parts of the offical couples, some people find Xanthe, Rhys and Reed to be so utterly unsympathetic that it damages their enjoyment of the comic and even drives them away from it.
Unfortunate Implications: Let's just say the webcomic isn't very "kind" to female characters, neither is it to the kinky and the mentally ill. Also, the brothel setting may come with its own can of worms.