Adaptation Displacement: The anime is far more well-known than the manga it's based off of, partially because of Kyoto Animation's big name, but mostly because the factor it's famous for (the stockpile of anime-related Shout-Outs) is almost entirely anime-original. As far as the U.S. and other western countries is concerned, you'd be hard-pressed to find anyone who even knows the manga at all.
Audience-Alienating Premise: The show was made specifically with otaku on mind, and was best marketed in America by DVD like nearly everything else from Japan. It's about high school girls, but the way they look, sound, and speak, along with the aesthetics in general, makes them seem like grade schoolers in what would seem to belong on Nick Jr., where it would actually have to undergo some kind of butchery first to land. Some of the things the girls talk about range from things that real teens don't (case in point: How does one eat such-and-such?) to references to yaoi, breast sizes, and kidnappings. Incompatible subjects for the same show, much?
Kanata Izumi, as despite only appearing in one episode and some minor cameos on photos, she's well remembered for appearing in one of the most touching and praised scenes in the anime.
Meito Anizawa. The Domon Kasshu lookalike and the manager of the Anime store that Konata frequents. He and his staff treat Konata as the most valued customer, codenaming her "Legendary Girl A" and always go to extravagant lengths to make her buy something, even resorting to militaristic approaches, while constantly shouting enthusiastic in typical anime fashion when trying to promote something.
Yukari, amongst the older readers, for being the darned cutest and most huggable mommy in anime (well, except maybe Akiko Minase.)
An unnamed (gasp!) boy appeared in one scene of manga Vol. 6. Apparently he was VP of Miyuki's class and wanted to confess to her but never did. Unsurprisingly, some fanart of him and Miyuki has sprung up. He's been given the name Toshiaki, which is basically the 2Chan version of "Anon".
Every main character that isn't Soujiro can be seen as Moe by someone (probably a result of Puni Plush) Konata outright designates Miyuki and Yutaka as walking Moe. And let's not forget that Kagami even won the 2008 Saimoe Tournament.
This series is commonly accused to be this. This may be the result of narrow focus; Comptiq after all is a video game/manga magazine and comic strips on that kind of magazine is supposed to be like that...
The anime is accused of this more with all the Les Yay and Shout Outs (even compared to the manga)
Poor Tsukasa, whom the directors of the show REALLY get a kick out of portraying as a helpless little girl who is LITERALLY pushed around in a big man's world. Even though this does make her even more adorable.
Kagami also counts to a lesser extent. She who has to put up with constant abuse from Konata and never gets into the class she wants, not to mention her adorable Cry Cute moments.
Also when dere-dere Kagami expresses her insecurities or wants that she can't bring herself to show. Yet again for Kagami during the episode where she has to put up with her (also Tsundere) big sister. She seemed at the verge of tears at one point. *runs to hug*
Also Minami in the manga; she's often mistaken to be the one behind many no-nos, such as not cleaning up after her dog, or a prank involving pressing all the buttons in an elevator.
Kanata Izumi, as despite accepting the fact that she has passed away, she still laments that she couldn't be with her family anymore and only able to visit them without any way to interact with them outside of spooky photos.