Melanie being brought in for a performance review that has Elias implant knowledge of how her father actually died, reducing her to a sobbing wreck? Horrifying. Elias saying that she can take the rest of the day off because of the state she's in, and actually sounding somewhat concerned? Horrifying, but kind of funny.
Elias's commitment to making his service of the Beholding as bureaucratic and managerial as possible is full of this. Sending the archive crew on a half baked scheme to stop the Unknowing, and openly making plans for their replacement if they die in the process? A chilling reminder of how everyone is disposable to him. Following that up by reminding them to save receipts if they want to be reimbursed for their expense in case they do survive? Hilarious.
Peter Lukas is full of this. Him and Martin wandering through the maze-like underground of the Archives and holding a Leitner, unsettling. His cheery reply that the blood on the book is a Leitner too? Crosses it back to funny.
Daisy and Basira's relationship is left ambiguous, but it's clear that they've been very close for many years; quite a few fans like to speculate that they were romantically involved while working for Section 31.
The Magnus Archives being a podcast and all, listeners have little to no idea what the characters look like. Nevertheless, Jon is almost invariably portrayed in fan art as having light brown skin, short black hair, and always wearing glasses and a green sweater, as well as various scars from the times avatars have beaten him up. Martin is portrayed as having curly red hair and a short nose, and is generally either tall and skinny or short and round (depending on how the artist interprets "not the smallest guy"). Anything Beholding-associated is usually green, often the same green as the show's logo, despite the fact the Beholding iconography is never described in more detail than "an eye".
In fanart, Basira is almost always portrayed with a Muslim headcovering of some kind, usually either a Hijab or Al-Amira, despite the fact that there's not any indication that she's actually Muslim beyond her name.
When the Web Table is delivered to the Magnus Archives, several characters bring up the possibility of destroying it while Jon disagrees with the idea of destroying knowledge. Jon later destroys the table and shows that was the worst thing to do when he accidentally releases the Not Them.
The Reveal in Episode 160 that the reason all the rituals have failed is because a single Power cannot be brought into the world due its connection to the other powers. This means all the sacrifices to stop the rituals - including Tim and Micheal - were all for nothing. Worse, by trying to prevent rituals like the Unknowing, Jon played into Elias' hands in successfully bringing all the Powers into the world.
Hilarious in Hindsight: Elias laments that Melanie can no longer fight after the ghost bullet is removed, saying that the Institute needs fighters and Jon can't record enemies to death. He does close enough to Breekon in the following episode and actually kills Peter Lukas when Peter resists his compulsion abilities.
I Knew It!: Several fans predicted that Elias was actually a vessel for Jonah Magnus long before Episode 158. Likewise, the theory that the Beholding ritual could only go ahead after Jon got a mark from each Power was widespread before Episode 160 dropped.
Martin is a kind, unsuspecting archival assistant with a penchant for bad poetry and crush on Jon. He gets put through the wringer multiple times, from being trapped in his apartment by Jane Prentiss for weeks, to having his darkest traumas brought up by Elias. He doesn't let any of that stop him, though.
Gerard Keay has spent the majority of his life under her mother's thumb, unable to leave due to his knowledge about the powers making having a normal life difficult, even more so after he was nearly convicted for her "murder". But unlike most others forced into this life, when he appears in statements he's often helping others or destroying the Leitners his mother was obsessed with and was assisting Gertrude when she was looking into how to stop The Unknowing before allegedly dying of a brain tumor at a relatively young age. He's more of a Jerkass Woobie by the time Jon meets his spirit since Gertrude binding him to a book made existing painful and he's been used as a "monster manual" by Hunters ever since she left him behind.
Jerkass Woobie: Several character qualify, but especially members of the Archives staff.
Jonathan Sims is cantankerous and paranoid at times, but he also gets put through the wringer thanks to his position as head archivist, particularly by Season 3 where he's framed for murder, kidnapped and threatened by avatars of the Powers multiple times, and he's put into a coma where he's forced to watch nightmares of statements over and over.
Melanie and Tim. While they want to leave the Institute, they're unable to, making them more than a little bitter.
Magnificent Bastard: Jonah Magnus, who has arranged almost all of the major events of the series, manipulating Jon into becoming the Archivist and releasing all of the Powers.
Joshua Gillsepie, despite only appearing in a single episode, is treated by the fanbase as a genius, and is one of the most beloved one-shot statement givers due to his admittedly very smart handling of the coffin that was delivered to him.
Peter and Elias have never actually talked to each other "on-screen" until 158, anyway, but given their similarities (both Affably Evil and extremely powerful) and the possibilities for hilarious personality clashes (Elias seems more serious, while Peter is faux-cheerful), plus the fact they apparently have an alliance going on, it's a fairly popular ship.
To a lesser extent Gerard and Micheal are a surprisingly popular pair for a guy who's allegedly been dead for years before the series started and an active but inhuman Wild Card. Whether it's due to both being popular characters on their own that are both currently out of the picture with the whole "being dead" thing and the latter replaced by Helen, the irony of putting a contrary monster with someone who knows how the powers it serves works, or their shared past traumas with Gertrude specifically can vary. Sometimes presented as having them know each other from when Micheal was still Gertrude's assistant, considering Gerard's father fondly remembers working with Shelley when his ghost asked Gertrude to take care of Gerard, who she hadn't met yet, that's very unlikely to have been the case.
Uncanny Valley: Pretty much everyone in the statements who's a servant of the Powers is described as having something off about them— too tall, too short, too broad, too thin, that kind of thing. Naturally, this is taken Up to Eleven with the servants of The Stranger.