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.
Alternative Character Interpretation: Chitanda suffers from some sort of neurological disorder that affects her memory and prevents her from maturing beyond the mentality of a four year old.
Also, Irisu is emotionally crippled due to being the heir to her family's business, meaning she has to shoulder the burden of running a company before she even graduates from school. The result is that she can't really make any meaningful relationships and comes off as a Manipulative Bitch. She is also secretly jealous of Chitanda's childlike innocence, as she represents the childhood she always wanted but can never have.
Base Breaker: Opinion on the ending of the anime is split between those fans who thought it ended on a logical and satisfying note to those who were disappointed that neither of the USTs were adequately resolved.
Oreki: I don't really care, but Chitanda got curious. I can't avoid it.
Mayaka: You should just ignore her then.
Oreki: The problem is that she's not someone I can ignore.
Episode 17: Satoshi is once again humiliated and out-shined by Oreki and just as he begins putting on his Jade-Colored Glasses, Mayaka gently tugs on his shirt, reminding him that there's still someone who will never think less of him.
And this, from the Finale:
Oreki: It's getting cold.
Chitanda: No— it's spring now.
Remembering Oreki's schpiel at the beginning of the series of a "rose-colored high school life", you can tell that he's definitely changed and embraces the rose-colored life; wrapping up the series with Book Ends.
Fridge Brilliance: Episode 22 features an Imagine Spot where Oreki indirectly confesses to Chitanda. The lighting in the scene is pink due to the cherry blossoms and sunset— he's imagining that rose-colored high school life!
Fridge Logic: In Episode 17, Satoshi would not have been wise to pound the flames engulfing the manuscript with his bare hands. Especially considering it was lit by spraying water onto a chunk of sodium hidden between the sheets. Anyone who has basic knowledge of chemistry would know that dousing their hands with concentrated sodium hydroxide is not quite a brilliant idea.
Harsher in Hindsight / Unfortunate Implications: Episodes 13 and 14 show students casually wielding a watergun which is a very convincing replica of a Glock pistol. In countries with a history of gun violence, such a thing may be very uncomfortable to watch.
Episode 17 definitely cements Tanabe Jirou as one. He plans and carries out the Jūmonji thefts in an elaborate ploy to get his student council president, Muneyoshi back into manga drawing. To Tanabe's dismay, It fails.
Memetic Sex God: In a certain Image Board, there were some board-goers going like "Hey let's ship him with everyone!" From within the same thread it produced fanarts of crossover couples such as (with the former being the one who leads on) Marika/Oreki and Oreki/Mio. Try looking for them in the archives if you know how to get there, and you'll see. First and foremost warning: said fan arts are NSFW in nature, so use discretion. To put it in simpler words:
"It's been long established that Oreki is instantly shippable with any other character. They're all OTPs before his swag. God help us if he ever decides to expend some energy." — Anonymous
Moe: Eru definitely qualifies, and to a slightly smaller extent, Mayaka does as well.
Ship Tease: Episode 3 makes it painfully obvious that Houtarou feels something for Eru, at least if the beginning sequence is to go by.
Episode 6 makes him excited at the prospect of her being a soulmate after she says something about wanting to embrace his lifestyle. He's genuinely disappointed that she's joking.
It's NOT teased that Ibara has a crush on Satoshi but neither has admitted to the other that yet. Episode 6 has Ibara yelling at him like a housewife, and the next minute they're sharing a laugh.
Episode 7 is the most blatant so far, with Houtarou passing out just from fantasizing about Chitanda in the bath, then blushing and flinching when she touches him. It probably didn't help that Chitanda expresses disappointment when she found out the hot springs wasn't a mixed bath.
Unusually enough, episode 10 seems to ship Irisu/Houtarou, much to the other shippers' despair. That is, until he figures out Irisu's true motives and completely (and justifiably) flips out at her.
It still doesn't stop them from being very, very imaginative.Sometime after episode 11 in which Oreki snapped at Irisu, someone posted a few shots of Irisu photoshopped with blushes, and later they went like "Her name is Surii, and she is Irisu's kinder twin." You could say the ship rose back again as a ghost ship.
Episode 11 has Satoshi asking where Mayaka is for some unknown reason, as well as the many segments of Houtarou and Eru talking, most obviously the one at the end.
Oh, man, the OVA. It's really hard to count how many times Oreki tried not to glance at Chitanda in her swimsuit.
In episode 13, Houtarou finds the photos of Eru cosplaying...yeah. It gets especially shippy near the end where Eru questions about it and they both start blushing.
Episode 14 features lots of Satoshi and Mayaka, especially near the end.
Meanwhile, episode 18 features Houtarou and Eru going on a pseudo-date, and from the looks of the preview the next episode is going to contain even more.
Episode 19 lives up to the promised Ship Tease. The episode consists entirely of Eru and Houtarou talking to each other, puzzling out a mysterious announcement to test his deductive abilities. The episode features Houtarou promising to accompany Eru on a visit to her uncle's grave, once again taking the initiative, two Almost Kisses, and Houtarou giving a genuine smile. And once again, the next episode promises even more.
Episode 22 has Houtaro nearly making an indirect confession to Eru, only to hold it back at the last second.
Episode 21 has Satoshi rejecting Ibara's Valentine's Day chocolates, then Ibara's second ones getting stolen, then Eru blaming herself from leaving the club door unlocked and supposedly hurting Ibara's feelings, then Satoshi revealing later that he stole them due to his inability to be close to anyone. Damn!