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.
Arc Fatigue: The childhood proposal mystery. Yes, the main plot. Over 100 chapters has gone by, and only a few details about it have been disclosed. That being said, the chapters that actually focus on the main plot are generally considered the best ones. The problem is that for each main story chapter there's at least five one shot chapters that serve little purpose beyond drawing out the manga.
What's more is that even the characters themselves are starting not to care, especially since it's starting to seem like Raku said it to more than one person. Whenever anyone mentions it now it tends to be about how much it doesn't matter.
Americans Hate Tingle: While Kosaki is popular with the Japanese fandom due to her Yamato Nadeshiko traits, topping character polls of the series, she is a much more divisive Base Breaker in Western fandom. In the latter fandom she's either "weak and boring" or "the only truly nice girl in the harem," with little middle ground.
Broken Base: Studio Shaft of all companies getting the rights to making the anime adaptation has caused a major split in the fandom. You're either on the side that enjoys the unique quirks they bring to the Rom-Com genre, or you're on the side that thinks SHAFT's style is just too much of an out-of-place distraction to fuse with this kind of story. The latter opinion only intensified with each Blu-Ray episode release, where the studio added all sorts of color filters to scenes that, in the original TV airing, looked completely normal, leaving watchers to wonder what the hell was the production thinking.
Fan-Preferred Couple: Several fans, partly due to Arc Fatigue and frustration with ever-complicating harem hijinks, have expressed the desire for the story to focus more on Shuu/Ruri than any of the potential couplings of the main characters. To the point that many such fans subjected Raku to some Die for Our Ship when chapters 113-114 looked like it was a set-up for Ruri to join his harem, although this sentiment was mitigated with the presence of Shuu and the Ship Tease resolution with him in chapter 115.
Hollywood Homely: People sometimes wonder how someone who looks like Raku could end up with girls like Chitoge. This trope is zig-zagged though, since it's revealed he was actually quite popular amongst the girls in middle school.
Idiot Plot: Chapter 52, where Raku has to find out Chitoge's measurements in order to open a briefcase. He figures that asking her upfront would label him as a pervert. So what does he do? He sneaks into the girl's room during their physicals, followed by disguising himself as a doctor to look at the charts. And when that all fails, he decides to finally ask her directly. By shouting it as loud as possible in a room filled with changing girls. It's even lampshaded by Raku himself at one point as he wonders why he decided to sneak into the girl's room in the first place.
Marika's friend Mikage is described as being a "dirty old man" and is possibly an outright lesbian and it's hinted that the person she likes is Marika, though she says she's saving herself for Johnny Depp.
Haru's friend Fuu-Chan has some strong feelings for Haru. There is also Haru's slight obsession with becoming friends with Paula.
An extra has Fuu-chan taking pictures of Haru in exceedingly sexy poses, after they're done Haru asks Fuu-chan if she's okay because her nose is bleeding, basically confirming her being gay for Haru.
Chitoge's Character Development with Raku aside, it helps that later chapters caused people to begin to switch their dislike for Chitoge's bitchy attitude over to Haru moments after the latter was introduced.
Haru eventually as well, basically turning her character into a Tsundere Onodera after she finally starts to come around regarding how she views Raku.
Values Dissonance: To western viewers it can seem very strange that Kyokou-sensei would quit her job just because she was getting married, or that during the career counciling in 122 marriage would be seen as an alternative to a career instead of a seperate issue. While it is uncommon, but not unheard of, for a woman to quit her job in The West due to getting married, pregnancy is usally the more deciding factor, or more cynical, the husbands income, in Japan and Eastern countries it's common enough to be expected.
What an Idiot: Most of the times, Raku is an Accidental Pervert due to situations beyond his own control. This is not the case in Chapter 52, where he invites it upon himself after pulling one stupid antic after the other.
Woolseyism: Marika's proper speech is translated into English as a southern-US accent.