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.
Audience-Alienating Premise: It's a realistic story about transsexuality and puberty, that includes other parts of the LGBT. So many people are used to the slapstick "He's a trap!" type series that Wandering Son comes off as this, especially to people clueless and ignorant about transgender issues.
Badass Decay: You'll often hear complaints how in elementary Takatsuki was a confident badass who beat up boys and stood up for her friends but by the end of the story she's far less secure in herself. In-series it makes sense but that doesn't make fans less sour.
Broken Base: The way Takatsuki is treated after middle school is polarizing within the fandom.
Ensemble Darkhorse: Chizuru is quite popular, at least in the anime, despite her lack of focus.
Many fans are calling Death of the Authorabout Takatsuki not considering themselves a boy by the end of the manga. Also to a lesser extent because Takatsuki/Saori never occurred.
Faux Symbolism: Almost all colored artworks show the boy uniforms as being pastel colors, when they're traditionally black. The anime, and the shading used in the manga, imply that they are black. It could be symbolically referring to their personalities but it seems like it's just for artistic value (the artworks often are watercolored too, so it's a theme). Though considering how Shimura is with shading, they really could be pastel.
Foe Yay: Takatsuki and Chiba in middle school, Doi and Shuuichi.
Internet Backdraft: Going onto /a/ on a Tuesday (or Wednesday), going into a "Taka Tuesday" thread, and even mentioning hentai isn't exactly a good idea. You'll get near Yotsuba&! levels of backlash and Squick. On a more general note, it's not best to try and discuss the characters sexual orientations if you don't want a debate to arise.
It Was His Sled: It's hard to discuss the manga without mentioning Takatsuki not wanting to live as a boy by the end.
LGBT Fanbase: If you're in the trans sphere some of the series (and the main/character pages attempts to describe whats going on with the gender stuff) will make you cringe in sympathy.
Mainstream Obscurity: It's known as one of the best depictions of transsexuality in fiction, especially manga, but few people have read past elementary or more than a dozen chapters.
Misaimed Fandom: Aside from what's mentioned above, a part of the fanbase believes it's a Shoujo romance manga, when it's Seinen and not romantic.
Pronoun Trouble: While not strictly a YMMV Trope, with this series the issue tends to be within the fandom than in-story.
There's been discussion on the wiki about whether to refer to the transgender characters by their biological sex (Nitori is "he" & Takatsuki is "she") or by their correct mental genders (Nitori is "she" & Takatsuki is "he"). As noted in the main page, the general consensus, for the sake of simplicity, is to simply match what's used in-story (Shuuichi "he" / Yoshino "she").
An argument against this consensus is that what is used in the manga technically shouldn't control how the audience refers to them because we have more knowledge about them than other characters within the series, and even though they are still closeted there is no good excuse not to respect their proper genders when we have the information to know better, "getting the surgery" is not a factor when deciding if you should call someone by the correct pronouns, and is a cissexist sentiment.
But as readers we do see what's going on inside the characters' heads, and they don't think of themselves as other than their assigned gender but rather as wanting to be other than their assigned gender. You can argue that this is a limitation based on their social upbringing in a cissexist society (and it definitely is), but if the use of pronouns is to reflect the way the characters consider themselves, then respecting their still-nascent understandings of their gender identity should also be important. If they are still using their assigned gender pronouns in their own thoughts, then switching the pronouns to fit the Western understanding of how gender works can become an ethnocentric imposition. Regardless — it's a tricky question, and very emotional for people who've been in Nitori and Takatsuki's situation.
Either way, there's little argument with Yuki. Yuki is more straightforward in that she lives as a woman, is implied to have had surgery, and everyone in-story refers to her as "she".
Takatsuki at the end of the manga. Fans don't know what pronoun to use anymore, especially to avoid spoilers.
Rescued from the Scrappy Heap: Chiba. After several volumes of being The Scrappy due to her temper and attitude, she was rescued near the end of middle school when she began cooling her head and rekindling her friendships.
Fumiya was redeemed after years of Saori's harsh remarks pointed at him seemingly got through to him, and the guy finally realized that he could be viewed as annoying.
They Wasted a Perfectly Good Plot: In high school Saori begins dating Fumiya with no pretense of liking him and the whole deal comes off as very "Why not?" Saori was never shown to be a terribly good girlfriend and they got no screentime romance which made fans think she didn't love him. Nope, they never break up or shown any signs of wanting to.
Takatsuki in late high school It's eventually decided she'd rather live as a girl, though whether that's true or not is a Base Breaker. The manga treats being feminine with being a girl, instead of letting her stay masculine/androgynous and saying she's a girl despite her gender presentation.Aoi Hana had a similar issue with a butch character.
The fact that she was the only transman in the story left a bad taste in a few reader's mouths.
This gets even more unfortunate if you know that a common stereotype about transmen is that they're just insecure girls who hate their femininity.
Many people have been squicked by Yuki and her near-pedo behavior towards Takatsuki, even if it's non serious teasing. It doesn't help that then transsexual character is seen as the pedophile.