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.
Base Breaker: Jack Vessalius became one after Retrace 65's Reveal. Either everyone hates him now for having lied throughout the whole manga and, recently, for his treatment towards Oz or still (or started to) love him, because of the depth his character has gained from said Reveal.
The chapter in which the core cast (except Oz and Break) all get drunk can be counted as one for the following reasons: it was full of randomness, it brought little to no contribution to the plot, and it is never mentioned again afterwards.
Cargo Ship: As revealed in Chapter 71, Oz was originally a pair of stuffed rabbit dolls. Do the math. Especially since Alice owned one of his bodies.
Other ships include Oz x the cookies he found in the Abyss, Alice x meat, Gilbert x his hat, and the list goes on...
Complete Monster: Isla Yura manipulated dozens of politically powerful people into believing that the Abyss was a paradise, even though he knew just what kind of a hellish prison the Abyss actually was. Using one of these connections, he was able to gain control of the abyss-sensitive children of Fianna House, and he tricked them into contracting with the chain Humpty Dumpty, a contract that would eventually kill them. He then used these contracted children as Brainwashed and CrazyChild Soldiers to slaughter dozens, maybe even hundreds of people as preparation for a second Tragedy of Sablier, and he did all this because his greatest wish was to die laughing in the face of the unknown, and the Abyss was the greatest unknown. Which is fine in and of itself, but the only way he knew how to go to the Abyss was by trying to annihilate a country, so that's what he did. Needless to say, he didn't regret a thing.
Glen Baskerville also has his fangirls. Specifically, all the Glens have his own fangirls.
Foe Yay: Break and Lottie had some before and during the Isla Yura Mansion arc, but as they haven't interacted since, we can't say for sure where this is going.
Vincent also seems to have some sort of fixation on Break, having once told him, "I like you the most." Hell, an official guidebook had Break in both Vincent's "likes" list and in his dislikes list. For his part, Break despises Vincent and wants nothing more than to kill him for poisoning Sharon.
Harsher in Hindsight: In Retrace IX, Break comments to Oz about not being able to see him (referencing his strangeness). Alice responds to this by mocking him, asking if his eyes have rotted out. Fast forward to Retrace XLII, where the decaying of Break's body causes him to go blind.
HSQ: Ever since Retrace 57, chapters that invoke exponentially high levels of this have gotten much too common for the fandom to handle, but special mention goes to...
Retrace 65, from page 51 on. Whoa nelly, make sure your grandmother's not in the room when you read this one. It's the Plot Twist to end all plot twists.
As of Retrace 70, Oz is apparently B-Rabbit, and his body is actually Jack's body. Raise your hand if you saw that coming.
After several chapters of important plot exposition and build-up, Retrace 74 gives us Echo showing up, the multiple revelations of what really happened during the Tragedy of Sablier, Jack effectively beginning the countdown to the end of the world, Oz apparently getting his body back only to hit a Heroic BSOD, and Leo is alive, appears to have been taken over by Glen, and has poor Oz shot in the chest in the middle of said Heroic BSOD. By Gilbert. Feeling breathless? We don't blame you.
Sharon likes to dress Alice up and even got her to call her big sister.
The first novel also had a moment involving Sharon, Alice and some lesbian porn. Granted, Break was the one who initiated the moment and Alice didn't know exactly what she was doing, but still!
And in the anime, there's also Lottie, Ada, and the poison. Not that I'm complaining, Heavens no!
Magnificent Bastard: We have three examples, two of them borderline and one of them played to the hilt:
Xerxes Break shows shades of this, what with how he's always planning things out and subtly manipulating his friends to push them down the path he wants them to take, but overall, he's not as in control of most situations as most examples of this trope need to be.
Rufus Barma is the straightest example in the series. While at first he seems like just an information broker, albeit a manipulative one who knows a lot more than he lets on, after the incident at Isla Yura's mansion, he shows his true colours by helping the Baskervilles take down Pandora and personally taking Break out of the fight by destroying the Rainsworth's Key to the Abyss, severing Break's, Sharon's, and Sheryl's contracts with their chains. Then, as of Chapter 86, the true depths of his Magnificent Bastardry are shown when it's revealed that he played the Baskervilles for fools: he never betrayed Pandora, he just knew that the Baskervilles would invade anyway and inflict massive casualties, so he took measures to keep as many of Pandora's men alive as possible. He didn't break the Rainsworth's key, he broke the Barma's, and in doing so robbed Glen of the power of Dodo. He also sent Reim the Rainsworth Key, which allowed him to repair the Rainsworth contracts, namely Break's with the Mad Hatter. Because of him, the majority of the Baskervilles were separated from their leadership with Break, and seemingly Pandora, on the counterattack.
The Most Jarring Example is Jack Vessalius the instigator of the Tragedy and used everybody as pawns to send the world into he abyss for his twisted obsession with Lacie.
Memetic Molester: Break will appear under your bed without warning! The fact that he's fond of giving younger characters candy doesn't help.
Vincent and Lottie, the king and queen of badtouch.
Glen/Revis became this ever since it turned out that he impregnated Lacie. He'd definitely like to have an "experiment" with you as well.
Moral Event Horizon: Very little of what appears to be evil in this series is actually as bad as it seems, but some things still stand out:
Isla Yura trying to start a second Tragedy of Sablier and brainwashing innocent children to do so.
Xai Vessalius murdering his own brother in cold blood.
Moe: Little Gilbert. And then Oz puts him in situations that only increase his moe-ness. Also, Oz in a maid dress.
There's Lily, too. That is, whenever she's not busy being a Creepy Child.
Alice is also this whenever she's excited, like in one omake which showcases just how much she liked getting pat on by Gilbert.
Reread Bonus: The manga can be quite the Mind Screw, especially if you read it the chapters as they come out at a rate of once per month. Reading it again won't be as suspenseful, but it'll make a lot more sense. It's also typically a good idea to read the previous five or so chapters before you read each new chapter so that you remember exactly what's happened, cause this manga loves to use some really subtle Chekhov's Guns.
Ugly Cute: Rufus Barma. Specifically, the first form Oz and the gang meet him with.
Oz, his father has ignored him his whole life and was the very person who sent him into the Abyss.
Gilbert and Vince too. Say what you will, but those two have gone to hell and back.
Leo too. His best friend is now dead, and he feels like everything that's gone wrong is all his fault. That's not getting to the many orphan children (who he cares for enough to consider his siblings) dying.
Alice, Break, Echo... it's actually easier to count who isn't a Woobie.
Elliot deserves repeating. It's pretty clear the author loves to torture her characters, but Elliot gets the brunt of it by far.