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.
Fan Hater: Kirino fans tend to also like Kuroneko for the most part. Kuroneko fans tend to really hate Kirino, which results in Kirino fans hating Kuroneko fans for hating Kirino, despite largely liking Kuroneko themselves. Then you get the Kirino haters who don't much like Kuroneko either...It's as headache inducing as it sounds.
There was a rumor started that Volume 8 had Kyousuke dumping Kuroneko and her being put on a bus, which lead to some fans tearing up their novels before they'd even read it. If they had read it however, they would have found that Kuroneko's the one who dumps Kyousuke, and she isn't moving away permanently, but won't be going to his school anymore either. Red faces all around. Some fans who tore their novel up even went so far as to fix it with sellotape or similar means.
Love It or Hate It: Reactions towards the ending. Let's just say the people who were rooting for anyone other than Kirino or really didn't like incest hated it, while those in camp Kirino adored it. To make it even more complicated, the Kirino camp is split into two factions: those who were simply happy that she ended up with Kyousuke, and those who didn't like the fact that Kyousuke alienated practically all the other girls in the process of getting together with her, and then decided that they'll go back to being 'normal' siblings after graduation.
Kirino manages to outdo even Ayase in an If route of the same Visual Novel, being turned into a yandere Green-Eyed Monster by a wish Akagi made concerning little sisters, with Kyousuke implied to have been crippled or killed by her to keep anyone else from seeing her precious Onii-chan.
Despite being the title character, a number of fans are put off by Kirino's initially Jerkass behavior and her poor treatment of Kyousuke, who is practically throwing away any chance to be seen as normal for her sake. This reaction tends to vary between fans coming from the anime (where her tsuntsun bad behavior is kicked Up to Eleven), the Light Novel source which is more evenly balanced, and the manga where her words aren't as harsh and her mannerisms are much more deredere in response to Kyousuke's actions.
This is actually intentional as even characters in the novel think the same thing, but tend to see the glass half full and that Kirino is, while annoying, still important to them.
Ayase's extremely judgemental nature of Kirino's hobby has earned her numerous haters even among those who alsoconsider Kirino a Scrappy. Like Kirino, she's grown out of this, and her scary moments, when they show up, are always played for laughs or d'awws after the initial conflict is resolved.
Manami has managed to become one of the most hated characters thanks to the events of volume 11, where it's revealed that she is the cause of Kyousuke becoming the useless guy that he is today, and being the catalyst behind the strain in his and Kirino's relationship. Her fight with Kirino at the end certainly didn't help matters.
Ship-to-Ship Combat: One is for Brother-Sister Incest, the other is against. Within the latter groups, there are fans for Kyousuke-Manami (who consider her the most sane and normal of the choices) against fans for Kyousuke-Kuroneko/Ayase/other girls (who are seen as the more interesting choices).
So Bad, It's Good: The 3-part finale, especially the final fight between Kirino and Minami.
In the series, Kyousuke eventually moves out temporarily for his studies. This is a monumental occasion for most young men, regardless of circumstance, and in most cases comes with a great amount of drama in real life, let alone television. The anime skips over the entire moving out process and goes from him being kicked out to him living alone in his small flat.
In the same episode that happens, Kanako mentions in a throw-away line that her home situation was so bad that she ran away to live with her sister and is now trying to find a way to make up with them. Again, this has no build-up or acknowledgement within the episode at all.
To a lot of Western viewers, Kirino and Kyousuke's dad could be considered abusive. In addition to being cold to his children, at one point he punches Kyousuke in the face strong enough to knock him down. In addition, Kyousuke's mother has a fairly hands-off approach to child-rearing, although this isn't nearly as controversial. She only steps in when she mistakes the fake-dating ploy for an incestuous relationship.
And in context, Kyousuke was clearly trying to get a rise out of his father, and to his credit his dad accepted Kyosuke's impassioned defense of the hobby immediately after. So in essence, the message is, "This is for violating my rules and daring to have an opinion. Now do whatever it was that made you feel good and what you think is right in a responsible manner."
At a later point in the series, Kyousuke's parents actually kick him out of the house to make him study (and Kyousuke wasn't a particularly bad student), not letting him back until he finishes his preparatory exams. No-one has any problems with this. His mom has the added justification of suspecting him and his sister of incest, but that may very well be an excuse.
Kirino's love for cute two-dimensional girls could indicate that she is inclined to have romantic feelings toward people of her own gender in real life. At one point she even gets addicted to a game with a virtual girlfriend, who she is openly smitten with, and who also happens to look a lot like her best friend Ayase. Alas, suggestions that Kirono might be lesbian or bisexual are usually met with rather dismissive responses, including from her best friends and Kyousuke. Seeing how severe Kirino's parents tend to respond to fairly benign matters, one can only dread what they would do if Kirino would come out of the closet.