Shinichi jumps into a burning building in Episode 12 to save a copy of this "rare" issue. He also mentions it in the classroom before it burns down. Given this is a show with parody and otaku historical moments, what event is this referring to?
This year's October issue of Comptiq magazine was in extremely high demand because it came with a bonus artbook for Kantai Collection, a web game featuring naval vessels as cute girls,1 which is the latest mega-craze among otaku in Japan.2 Apparently, tons of people were hoarding this issue in order to get multiple copies of the artbook.3 The character on the right side of the cover is a parody of Kongou, a popular character from Kantai Collection.
Quite a timely joke, really.
Addendum: here are the covers of the parody of Comptiq ("Comptiqle"?) shown in the show and the actual Oct 2013 issue of Comptiq. (Click to view full-size.)
1 Not to be confused with the other thing featuring naval vessels as cute girls, Arpeggio of Blue Steel.
3 See, for example, this piece: Havoc Ensues Over Battleship Bishoujos (warning: SeventhStyle; NSFW). Because SeventhStyle is awful (but unfortunately the only English-language commentator on this I can find), here is some episodic commentary that mentions the joke (in Japanese): some blog; some other blog.