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.
Punpun's mom. At times, she may seem to border Evil Matriarch levels. At times, she seems to just be grumpy. Besides Punpun, she is without a doubt the most conflicted character within the series.
The ending leaves itself open for interpretation. Is it a happy ending because Punpun seems to be going down a path of normal and sanity now, or is he just a hollow shell who keeps marching on because he isn't even strong enough to kill himself?
Aiko gets a lot of this, particularly in later chapters. For example, whether or not many of her actions are an understandable effect of being a constant victim of abuse, or just plain and genuinely twisted and unforgivable, is a subject of debate. Punpun's own actions, which come from similar causes, are also debated frequently.
Base Breaker: Aiko. A lot of people dislike her for screwing up Punpun, and being the catalyst for a lot of his poor decisions and darker moments, even if she didn't want that to happen; but some find her an incredibly tragic woobie due to her past.
Darkness-Induced Audience Apathy: Has been known to happen. The manga as a whole has a very positive reputation as being exceptionally well-drawn and masterfully written, but the story eventually becomes so relentless and depressing that it can turn people off. In particular some people feel that Punpun becomes such a horrendous individual that they find it hard to excuse his behavior or care what becomes of him.
Ho Yay: The end page of chapter 104 depicts Aiko and Sachi cuddling together.
Seki and Shimizu have a very strong relationship as a result of the former saving the latter's life from a fire (which results with both holding hands and Seki looking embarrassedly to the side). They are the only friends from the group to remain close throughout their teenage years, keeping each other grounded. Seki's girlfriend once asked if he was gay from how much he talked about Shimizu.
Magnum Opus: For Inio Asano. Solanin is also widely acclaimed, but Punpun seems to be more popular, and is a more "epic" and ambitious story, being the longest of Asano's works.
The sex scene in chapter 36 is... rather disturbing to look at. What the characters are saying doesn't do much to lighten it up, either.
What Punpun looks like when he snaps in volume 9. He becomes this black mass with too many eyes, and tends to spout lots of nihilistic quotes whenever he's depicted like this.
It gets worse in volume 11, after he kills Aiko's mother, when the latter tried to stab Aiko, and in volume 12, when he beats someone up for criticizing Sachi's manga (among other things), and later tries to kill Aiko, and then himself, in absolute grief over his murder.
And then we get this frame◊ as Punpun beats up the guy in volume 12.
Squick: In chapter 137, Punpun and Aiko have sex in a forest. And right after a very disturbing emotional confrontation between the two of them, at that.
The Woobie: Aiko. She had, by far, the shittiest life of anyone in the story. And it ends in the worst fucking way possible.
True Art Is Angsty: The manga is frequently considered a masterpiece by those who read it, and is praised for its lifelike characters, strong art, and skillful visual storytelling. It's also relentlessly dark, cynical, and sometimes even nihilistic.