Badass Decay: Nyaro takes this to the logical extreme. At the beginning of the episode, he is introduced after having slain several gods, with bad lighting that barely reveals his features and apparently reveling in the carnage. By the end of the episode, he's been chased by the police, defeated several times by accident, and his One-Winged Angel form blasts off after basically having his toe stubbed. He actually puts up some of a fight in the light novels, but Nyarko still hands him his ass and sends him blasting off at the end.
Having a male character (Mahiro) hitting female characters (Nyaruko and Cuuko) treated as comedy received mixed reactions from the audience.
On one side there are those who welcome the change since in most anime and manga, it is usually the female character hitting the male character being treated as played for laughs. They just want to watch something different from the usual.
On the other side, there are those who disapprove male-on-female violence even for comedy purposes. They typically tend to show love and/or sympathy towards Nyaruko while expressing their dislike to even downright hate towards Mahiro.
Crack Pairing: Considering the main pair is a human and an Outer God, you'd think this be enough. But there's also Cthugha x Nyarlathotep. In the regular Mythos, one was used to fight off the other; in Nyarko, this is acknowledged as the two races being bitter enemies. On top of that, Nyarko is utterly repulsed by Cuuko's advances, and she originally threatened to kill Mahiro, so all told Nyarko has some pretty solid reasons to not wanting Cuuko around.
Considering the official explanation that aliens love Earth culture, all of the show's copious references can easily be explained as the alien characters being total Otaku who love to pepper their daily conversations with lines from their favorite shows — just like Nyarko does.
A rare example of this happening in the theme song, specifically, the ending of the first season, "Zutto Be With You". Nearly every single line ends with the sound "Oo". Try singing it out loud. Your face will look like you're desperately trying to blow someone a kiss.
In the Dating Sim episode, Mahiro is unwillingly jumped around between the key events of the game, skipping over large portions of the school year. We're never outright told how the others experience it, but the fact that Nyarko had the time to knit a (rather long) scarf for Mahiro's Christmas present implies they lived out the whole thing. That in and of itself is pretty scary, but then one has to wonder what happened to Mahiro in the meantime — did he simply disappear, or was he on "autopilot" like Adam Sandler's character in Click when he fast-forwarded time?
Fridge BrillianceandFridge Horror: The gods of the Cthulhu mythos love Earth's anime, manga, and games - especially, apparently, the hentai stuff based on the doujin Nyaruko was buying in episode one. What's hentai infamous for? Of course it would appeal to them!
Fridge Logic: Acknowledged in one of the Nyaruani shorts. Mahiro is reading the first light novel, and asks Cuuko some questions: she joined Nodens in order to see Nyarko again, and she got into the PDO thereafter thanks to an uncle who works in HR. If that's the case, he asks, why didn't she just join the PDO to begin with and not have to become a criminal? Cuuko responds by lighting Mahiro's book on fire, telling him it's a warning.
"Funny Aneurysm" Moment: In the first season, Nyarko gives Mahiro a Yes/No pillow that depicts her wearing black lingerie; the first time she actually wears that lingerie is during her off-mentioned emotional breakdown and Anguished Declaration of Love in the second season, where it's anything but sexy.
On top of that, her breakdown is caused by the fact that Mahiro isn't willing to definitively say whether he's attracted to Nyarko or not — in other words, because he won't just say "Yes" or "No".
Genius Bonus: In one episode, Nyarko performs Eiji Hino's transformation pose; the sharp-eyed viewer (and one familiar with Kamen Rider OOO) will notice that the energy rings that appear correspond to the Kuwagata (Stag Beetle), Tora (Tiger), and Condor Medals. Applying the naming convention used for OOO's forms, one gets Ku-To-Ru - the Japanese pronunciation for "Cthulhu".
Harsher in Hindsight: Or rather Creepier in Hindsight. Once you see Shantak-kun's human form, it becomes much harder to laugh at jokes involving its eggs, or how it snuck a sausage which was apparently laced with aphrodisiacs in Remember my Love(craft-sensei).
"The Reason You Suck" Speech Yoriko gives about how she thinks the Xoth-731 console is doomed to failure became a lot funnier after the reveal of the Xbox One at E3 2013.
In episode 1 of the second season, Mahiro adopts the Madness Mantra "It's just ink... it's just ink..." as Nyarko slaughters a Nightgaunt off-screen; jump ahead to episode 11 of Nyarko-San W, where the cast goes to a haunted house, and the mysterious stains on the carpet actually are ink.
A voice actress-related example with Rie Kugimiya. We know that she voices Hasuta. Then in 2015, she voiced a character named Annie Hastur in the Japanese dub of League of Legends.
The Strange Circumstances of one Mahiro Yasaka, as written by H.P. Lovecr/a/ft, from the /a/ board of 4chan, which is a re-imagining of the events of the episodes of the anime as if they were written and narrated by Lovecraft himself:
Mondegreen: A line in the first OP says "Chaos, chaos, I wanna chaos". However, the Engrish pronunciation makes it sound like "Gay horse, gay horse, I want a gay horse" to English speaking viewers. It's pretty much become a meme.
The second season OP has another one: "SAN-chi pinchi", for all its fame, starts to sound to English-speakers like "sons of bitches" after a while (though some viewers also hear "sandy beaches" or "sun peaches").
Nightmare Fuel: Mahiro finally having sex together with Nyaruko, in the sense that it ends with what may well be Death by Sex. Note: this is how the series ends.
That night, the screams echoed through Mahiro's room. "No!" 56 times, "Stop!" 23 times, "I'm dying!" an unmeasurable amount of times. They all belonged to Mahiro.
The Scrappy: Not a lot of people find Cunne's "incestuous Psycho Lesbian" very funny. The fact she is blatantly older than Cuuko only makes it worse.
The beach episode: Nyaruko's pestering Mahiro throughout the whole day, with him making more and more aggressive attempts to ignore her. She finally makes an offhand remark about how it almost seems like he doesn't like her, but she knows that's impossible...
They Wasted a Perfectly Good Plot: Not exactly plot, but more than a few fans feel that the Lovecraft references should have been better utilized. Some have even accused them of just being window dressing to make the series seem less generic.