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.
Akado Harue: Hands-off coach who lets her wards do their own thing, or frankly terrible club adviser who is never seen giving any good advice, or doing anything to shore up her girls' glaring (mental and playstyle) weaknesses?
This is deliberately ignoring the fact that, prior to Harue coming back to become Achiga's club adviser, none of the girls aside from Ako had actually played in a competitive environment before or, in Shizuno and Arata's cases, haven't played a game in years. That she was able to get them to prefecture-level preparedness in less than a month is nothing to sniff at.
Vindicated in Chapter 13. Harue really does coach her wards, and takes it very seriously. Unfortunately, it seemed that every other instance aside from the two shown in the chapter happened off-screen.
In-Universe, after the Achiga girls are told by Harue that they have virtually no chance of getting past the semi-finals and that same evening, overhear her discussing going pro, they wonder if Harue has essentially given up on them, and Arata, who by now otherwise trusts Harue, briefly wonders if this is the case after Harue says she won't ask about where or how they were training, but quickly puts it out of her mind. Ultimately, they decide to trust her after hearing that she'd turned down the offer to go pro for the moment.
Miyanaga Teru: Absolutely ruthless mahjong monster likened in-universe as a force of nature and by watchers as the on-table equivalent of Gilgamesh from Fate/Zero, or just an an extremely professional player who behind her stoic and uncaring facade is actually (as shown by her reactions in the last TV airing) a decent human being?
Evidence in support for the latter is even more pronounced in the equivalent chapter of the manga (chapter 12), where we're treated to Teru looking absolutely shocked at what happens after the Vanguard match. She also murmurs to herself that she wonders about how "that player from Senriyama" is doing.
Draco in Leather Pants: Teru has a ridiculously HUGE number of in-universe fans, despite being fairly a fairly cold person by nature(albeit not one without redeeming features). This is not necessarily extended to the other members of Shiraitodai.
Ensemble Darkhorse: Toki, with Kirame coming in a close second. Toki for giving her all, even risking her health to put up a fight against the monster of monsters Teru Miyanaga, despite the fact that she (technically) doesn't need to, and Kirame for her likeable personality, endless enthusiasm, and her unenviable role in making sure NO ONE goes under against Teru. Toki even went on to win Saimoe 2012, directly beating both Kuro and Nodoka from the same series.
Foe Yay: Senriyama's Hiroko has become "interested" in Arata (after noting her playing style and the odd distribution of draws, that is). When she's teased about it by a teammate, she doesn't deny it, and instead smiles knowingly.
Foe Yay Shipping: Sumire/Yuu is a somewhat popular pairing. It helps that Yuu spent time preparing for her match with Sumire while watching videos of Sumire playing.
Fridge Brilliance: Kuro's obsession with boobs might have a Freudian Excuse: her mother died when she was a very little girl, and thus she seeks the quality of a mother in her potential partner.
This is apparently confirmed in a manga that came with the BD releases, when Yuu tells the rest of their friends that to Kuro, large breasts remind her of their late mother.
Internet Backdraft: Shizu's performance in the final chapter did not make many happy, especially in the English-speaking fandom, since it goes against how she's been performing on the mahjong tables so far in the chapters preceding it (never won against a depowered Koromo or Kei, barely kept Achiga in the quarterlies due to crappy hands). The fact that she suddenly gains a game-breaking ability seemingly in the span of two chapters (and in less than a day in-universe at that) is considered such a massive Deus ex MachinaAss Pull.
Les Yay: Kuro seems to be very fond of boobs, especially Nodoka's. Watch out Saki, you have a contender.
Momo is more lovey-dovey than ever with Yumi, where they appear in chapter 7 (episode 8 of the anime). Yumi in particular doesn't seem to be bothered at all that Momo is pretty much humping her in clear view of the Achiga team.
Let me tell you about Ryuuka and Toki. The defining, and frequently reoccurring, image of them being Toki resting her head of Ryuuka's lap. It goes on from there.
Mairu and Himeko. The two have been friends ever since middle school, and their shared ability not only is said to run off the Power of Friendship, but also gives off "bondage" vibes.
Memetic Mutation: On the Japanese fandom's side (particularly on Pixiv), Ako being "cheap" and "easy". This was brought on by an unfortunate combination of her character design (which many seem to associate with girls who engage in Compensated Dating) and her play style focusing on low-value (or cheap) hands.
It's become fairly popular to parody the opening sequence with various other teams, often, the Kiyosumi team.
Moe: Most characters are moe in one way or another (Shizuno is determination-moe, Arata is bitterness-moe), but Toki and Yuu both take the proverbial cake with Ill Girl-moe. As mentioned before, Toki even managed to win the 2012 Saimoe Tournament.
Rescued from the Scrappy Heap: Kuro, somewhat; this is after she finally get her things together and is able to discard her cherished dora for the sake of stopping Teru. Additionally, some viewers also ended up feeling sorry for her rather than hating her for her poor performance, in part because some people hate her for it.
Kuro. It's clear that her mother's passing has deeply affected her in how she chooses to hold onto Dora tiles out of fear of parting ways with her again, as well as her recalling the other people who have come and gone in her life, particularly Nodoka. She also has the misfortune of facing strong opponents, particularly going up against both Teru and Toki in the semi-finals, and takes it quite hard when she loses points for the team.
Yuu, who not only lost her mother, but has been bullied as a young child because of her condition requiring her to dress warmly even in summer. She also is implied to have social awkwardness problems rivaling even those of Momo, as she had considered joining the mahjong club with her sister and the others, but felt as though she was unable to do so.
Woolseyism: In the Episode 6 preview, when Ako tells Shizuno to focus on the "flow" (pronounced "fuuro" in Japanese), Yuu says that she also works on her flow, and that she likes hot baths ("furo"), a bit of a pun. In the Crunchyroll subtitles, Yuu says she likes "the hot water flow", prompting Ako to say "Different flow..."