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.
The first OVA, in which Rito turns into a girl and his life suddenly becomes much more difficult.
In the OVA at least, this is balanced out with an Imagine Spot where, as a girl, Rito's life is much easier because all his Accidental Pervert moments are dismissed on account of gender.
Another instance in the manga, (Chapter 144), where a perverted spirit takes over Zastin's body and tries to undress every female he sees. He reveals that the reason he's gone rampant is because he was rejected by 500 different girls during his life, and agrees to leave if he can touch even one girl's breasts. Oshizu agrees, but just before the spirit touches her, she pulls the spirit out of Zastin's body and burns him away with spirit flame. The spirit's final words? "I knew it! Women are liars!" Considering the author's then-current situation with his ex-wife... (Although even Oshizu admits she did "something horrible" afterward).
Base Breaker: The Black Cat characters. Some Black Cat fans are annoyed with the changes made to their favorite characters, while others enjoy the alternate versions of them.
Die for Our Ship: Not quite as bad as some examples, but people were becoming very annoyed with Haruna as time wore on as she stood in the way of the popular Rito/Lala, Rito/Yui or Rito/Anyone-Other-Than-Haruna ships, really.
Yui, arguably the more well-received and popular female character of the cast. In one online poll of all the females, Yui came in first, with at least 50% more votes than the second place finisher. Fans love their tsunderes and Yui fits the archetype better than most other anime tsunderes out there.
Momo's wasn't doing too bad either in the original manga, but is nowhere near Yui's level.
The Not Herself chapter that had Haruna act like an evil sadist was pretty funny. Then it turns out the woman she was based on, the artist's ex-wife, rather than being a sweet Girl Next Door type was actually a hateful and sadistic woman that was also a philanderer, thief, kidnapper and extortionist. Maybe the writer was trying to tell him something...
The writer probably was: by the time he knew about it, Yui was written in more and more subsequent chapters and Haruna was written out. Undoubtedly, it's probably what led to Yui's Ensemble Darkhorse status, but one doesn't write out one of two female protagonists in favor of a secondary character without good reason.
The Scrappy: Meta-example. Yabuki's wife became absolutely loathed after fans found out what caused Yabuki to end the manga at first before Darkness came along. Yabuki based Haruna on his wife and she was ok with that at first. However at some point, she apparently had some form of breakdown and started making unreasonable demands about the character. In a drawn-out legal battle, Yabuki won only for his wife to kidnap their own daughter and demand money for the little girl. Yabuki gave in and surrendered a lot of money to get his daughter back safely. Other stuff followed on that, culminating in a divorce and the end of the first manga. This is also why in the Darkness manga, Haruna has taken the backseat and Ensemble Darkhorses Yui, Yami and Mikan have taken the front positions.
With the end of the manga, Kentaro Yabuki himself. His wife had been cheating on him, and he basically gave in to her every demand for the sake of his daughter. He could have fought his ex-wife in court for Lord knows how long but figured his daughter had suffered enough drama after being freaking kidnapped by her own mother. He chose his daughter's well-being over his own pride and perfectly justifiable rage. Papa Wolf indeed.