Anime Hair: Kagami has a rather outrageous quiff. So does Nanami, albeit lighter.
Asexual: Implied with Kagami, given his lack of reaction to all the fanservice around him.
Badass Bookworm: Kagami is so good at Science that he was able to prove a scientific theory without breaking a sweat when the best scientists in the world were having trouble disproving it. And yet he doesn't fear monsters like Seijuurou Nanamiand can take punches to the face and being whacked by a baseball bat on an everyday basis. Bad. Ass.
Demoted to Extra: More or less with everyone with an introduction arc devoted to them. After their initial arc, they don't have nearly as much screen time as they once did. Justified since the manga is already building up Loads and Loads of Characters.
Desperately Looking for a Purpose in Life: Initially, Kagami was forced by his sister to become a teacher to get him out of his NEET status, then was sacked barely a month after he started, then got offered a job for CERM, then got hired by an eccentric school chairman, then gladly accepts an offer from an old classmate of his after getting talked out of teaching by the CERM representative who came to his house earlier. Apparently, it is difficult for a hardcoreOtaku to get a life.
King Incognito: Chairman Hiiragi poses as a manga shoplifter in search for potential teachers for her school.
The Little Shop That Wasn't There Yesterday: In her attempt to place herself at the top 10 of Incho Academy, Kanan stumbled across the home tutor service which claims to have helped a lot of students ace their exams and subscribed to it. Turns out that the legendary tutor was actually Kagami.
Meido: Kiriko works part-time as one, which Makina uses as a ground to expel her from the school. Cue Kagami dragging Makina into a Meido on-the-job training so that she stops looking down on them.
Not What It Looks Like: When Minako and Kagami reunite, she cries about him not taking responsibility and quitting school over one of the most significant moments of her life. Right in front of his sister.
Teacher/Student Romance: It gets brought up from time to time that Kiriko and Kanan have feelings for him, most clearly during the Madoka arc. He also seems to unintentionally be gaining a harem with at least three girls so far - but this is also very much on the back burner.
Kotarou also seems to have feelings for him, quite possibly the mostextreme.