Aerith and Bob: In a way: most angels and demons have a proper angelic/demonic name and a common Japanese first name (Azazel Atsushi, Beelzebub Yuuichi, Undine Megumi, Salamander Kimitake, Moloch Yoshinobu, Zeruel Takeru, etc.). The angelic/demonic names function as surnames.
Indeed, while Sakuma does get along with Azazel, Beelzebub and most other demons, they don't particularly like her or care about her well-being, and they're sometimes seen plotting her and Akutabe's demise.
Animation Bump: Episodes 5 and 6 feature looser-than-usual animation direction by Chiaki Nakajima, who in the past has worked on The Tatami Galaxy and the token realistic Art Shift episode of Panty & Stocking with Garterbelt. As a result both episodes are some of the best looking in the show, with 6 having some of the most expressive and lively character movement in the TV series, not to mention some interesting scene composition and use of color.
AngelsAre Useless: The angels are just watchers unless they're fighting demons.
Archangel Lucifer: Lucifer is apparently not the king of the demons, but he is the highest ranking and probably most powerful demon. And he loves reminding others about this.
Baleful Polymorph: Sakuma is nearly turned into a cow by Moloch (in the first OVA) when she fails to provide him an adequate sacrifice.
Later she actually turns into a panda when Behemoth decides he doesn't want her sacrifice after all. She only turns back when Behemoth accidentally destroys the sacrifice, a PSP.
Berserk Button: Do not question Beelzebub's... peculiar eating habits.
Bratty Half-Pint: Koutarou, with the exception being that he dug himself out of his own mess when Sakuma and Akutabe didn't feel like helping him out.
Breaking the Fourth Wall: A number of times, most obviously when Lucifer specifies his sacrifice (marijuana leaves) and Azazel worries about the manga influencing the readers.
The Behemoth story, big time. A manga editor at Evening (the magazine Azazel-san is published in) wants to murder Kubo Yasuhisa and the entire plot revolves around Evening. Sakuma even likens a manga with half-assed artwork to Hunter × Hunter.
Butt Monkey: Sakuma and Azazel, the latter even more so.
Cosplay: Sakuma's forced into this so that she can get some notes for a test. She later joins for real once she finds out there is a profit to be made.
Crapsack School: Happens to Golgotha Middle School thanks to Undine.
The whole setting of the series can probably qualify as one.
Cute and Psycho: Beelzebub usually comes off as a pleasant (in his own way), well-mannered person... until he slips into the darker side of his persona, which is foul-mouthed, vulgar and violent.
Cute Little Fangs: Azazel's girlfriend, Kiyoko in her human form. Azazel himself has them as well but they're not very cute.
Dark and Troubled Past: Many members of the otaku circle Sakuma joins have suffered severe traumas due to bullying and other abuse in the past.
Deadly Gas: In his monstrous form Beelzebub's breath is comparable to really, really noxious gases.
Salamander's spit is awfully thick. And white. And sticky.
Sariel's hairstyle.
Strawberry Warrior licking the condensed milk off the strawberry in the mock opening...
Deranged Animation: The series is mostly realistic, as per Production I. G.'s usual art style. Oftentimes the animation goes nuts though, almost to Ren and Stimpy levels.
Executive Meddling: With the manga being what it is, the anime has been on the receiving end a lot during production to be fit to air on TV. In interviews various staff members asked Kubo Yasuhisa to write stories that can be adapted easier for TV.
Gratuitous English: Mostly the American "sumo wrestler" in volume 4, but Salamander also has a couple of instances. And Lucifer's tattoo says "God /bless/ fuck your ass".
Hey, It's That Voice!: The anime has a pretty impressive cast, for its genre and category. In the voice commentary the director said he'd been surprised that some of the more high-profile seiyuu (such as Rie Kugimiya or Keiji Fujiwara) accepted his offer.
Inconvenient Summons: The demons are often in the middle of something when they get summoned.
Played with when Sakuma summons Beelzebub while he and Lucifer are duking it out at full strength, saving the world of demons from serious damage.
The third time Azazel is summoned, he's having sex. The first time Beelzebub is summoned, he's on the john. Which actually makes for a good case of foreshadowing.
Invisible to Normals: The demons by default. They can make themselves visible at will.
It's All About Me: Lucifer. Oh Lucifer. But then, he represents Pride.
The sheer size of his ego makes him one of the few demons who are not intimidated by Akutabe.
Karmic Transformation: Happens to anyone who betrays the contract with their contracted demon without the protection of a grimoire. Like Okada and Himoi.
No Celebrities Were Harmed: Salamander's entire character is a parody of Yukio Mishima. (Although obviously he doesn't look like Mishima, being a small, red lizard, his fundoshi-and-katana outfit is a Shout Out to Mishima. His full name is Salamander Kimitake. Kimitake was Mishima's real first name.)
Otaku: Sakuma grudgingly cosplays for some in her university to get her hands on some notes.
Panda-ing To The Audience: Behemoth looks similar to a huge panda (with a trunk), and Sakuma gradually turns into a panda when Behemoth doesn't accept her sacrifice.
Rock Me, Asmodeus!: Lucifer tries to demonstrate his awesome guitar-playing skills to Akutabe, but his cute koala paws make it difficult. (He also wears leather pants and sunglasses, and has the ego of a rock star.)
Scaled Up: While fighting Beelzebub Lucifer turns into his true form, a huge black dragon.
Seppuku: Salamander tries to commit seppuku a couple of times, but never gets to go through with it.
Ship Tease: Akutabe and Sakuma, especially in episode 9 when Akutabe asks Beelzebub and Azazel to go see what Sakuma's up to when her work habits change.
In the manga Azazel implies that Akutabe just pretends to have a hands-off approach to Sakuma learning to be a demon summoner, and is actually watching her from the shadows. (Then again, it's Azazel who says this so it may or may not be true.)
Because of this he is the least popular demon in the manga among female readers. One of the reasons why the director of the anime gave the role to Kazuya Nakai was to boost Salamander's popularity. It worked.
He's so bad, the first thing he does to Sakuma when she greets him is spit on her face. Later, when the man who summoned him introduces himself to her, Salamander chastises him.
Stringy-Haired Ghost Girl: Sakuma claimed to be able to see one after Undine had "cured" her myopia.
Throw the Book at Them: Akutabe is fond of doing this to his demons, with the added effect that the books he uses are grimoires, and touching a grimoire has very painful consequences for demons.