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.
Better Than Canon: This is one of the very few instances of the anime being considered superior to the original manga.
Broken Base: Towards the ending and the revelation that Rin and Daikichi aren't blood-related and get married. Some took it alright while others tookit less than well.
Deader Than Disco: The manga's status in the west, to the point that its American publisher seems to be distancing itself from it. The anime is still regarded as very good, though.
Fanon Discontinuity: A good chunk of fans insist that the post-timeskip half of the manga never happened.
Fan-Preferred Couple: Daikichi/Kouki's mother. The anime, which cuts away the second half of the series, plays this up, in part because almost nobody liked Daikichi/Rin.
Hollywood Homely: Daikichi. There are several references in the manga and anime to him not only being shy and awkward around women but not all that physically attractive either, even though he doesn't look that bad.
It Was His Sled: Rin and Daikichi ending up together has been cited as one of the most poorly hidden manga ending spoilers.
It's not uncommon for the series to basically be referred to as "That manga where a man raises a little girl then ends up dating her 10 years later".
They Wasted a Perfectly Good Plot: The timeskip could have been a good way to show a single father's challenges with raising a pubescent daughter, along with expanding on Rin's bond with Daikichi at a more mature level.
Some feel that a teenage girl developing feelings for her adoptive father and how both of them deal with it might actually have been quite an interesting plot if it was handled...differently.
When Haruko runs away,the end of the episode/chapter has her deciding to just bear her unhappy marriage and relationship with her inlaws. She is not encouraged to fight for her own happiness despite the obstacles as the message of an American show might be. Deconstructed after the Time Skip, when Reina casually mentions that her parents separated at some point, suggesting that it wasn't the right path for Haruko.
On a related note, the scene when Daikichi's sister expresses concern about her fiance's desire to start a family immediately runs into some minor Values Dissonance. Daikichi does give her good advice (of the "talk to your husband, it's no use talking to me!" variety), but largely dismisses her concerns, deciding that the "leisure activities" his sister wants to keep are expendable — you have plenty of time to yourself at work, right? While very upbeat on one level, suggesting that spending all of your time at work or with your children in not automatically a huge sacrifice, a more Western audience would probably take her concerns more seriously and agree that someone who wanted to keep a free-wheeling lifestyle isn't yet cut out for motherhood — and it's unfair for her fiance to expect her to get pregnant, give birth, rearrange her lifestyle and cope. Of course, the fact that she's a bit of a Jerkass loses her sympathy points...and why is she marrying this guy if they've already got a massive difference of opinion on such a major issue?
Rin and Daikichi's relationship after the timeskip, though it's not so much that Japanese readers liked it but more that it was just bearable enough to be published.