These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Ensemble Darkhorse: Mayuyu by far has one of the most dedicated followings, despite the fact that she has little screentime compared to the other characters. However, being a Big EaterRobot Girl with an Arm Cannon and being based on one of the more popular AKB 48 members does tend to help.
Megumi has also picked up a small and dedicated following, being the only 76th generation understudy to get any sort of screen time and Character Development. Her Les Yay moments with Sae also certainly helped.
Family-Unfriendly Aesop: At least two episodes imply that you need to be selfish/greedy in order to accomplish your dreams. Indeed, episode 20 has Mimori after becoming Mariko Shinoda the 8th being portrayed as "sadistic" (supposedly as sadistic as the "real" Mariko Shinoda) by telling Kanata that if she want's to become a successor, she has to be "greedier".
The next episode seems to imply that you can only accomplish your dreams alone (i.e., without other people backing you up). At least, that was the conclusion Yuko came to when trying to figure out how to become the Center Nova, which was all brough on when the former Minami Minegishi the 5th told her about "Position Zero".
However, this is subverted later on when it's discovered that Yuko wasn't actually a true Center Nova, due to her refusal to recognize others.
"Funny Aneurysm" Moment: Episode 6's "I won't let anyone tarnish Sashiko's name!" Fast-forward to June 2012... the Real Life Sashiko gets caught in a scandal after a fan defames her in a tabloid, and she gets transferred to another group as punishment. Oops.
Mii-chan the 5th's whole role in Next Stage seems to echo creepily with her real-life love scandal. In episode 22 Ushiyama comments that Mii-chan seemed liable to fall for the wrong sort of guy. Also at the end Mii-chan muses that she'll have to start over from square one... just like when the real-life Minami Minegishi got demoted to kenkyuusei status after breaking the group's "no boyfriends" rule.
Iron Woobie: To state how much suffering Kanata goes through for nothing is an understatement.
Les Yay: Episode 10 has loads of this, specifically Kanata/Takamina, Suzuko/Makoto, and Nagisa/Chieri. The Real LifeAKB 48 is no stranger to do Les Yay moments.
Tear Jerker: Any dedicated AKB 48 fan probably choked up a little bit when Yuko told the girls that Acchan the 13th was the final center nova, and that no one would ever replace her—the Real Life Acchan had announced her graduation from AKB 48 only a month or so prior to the premiere of the anime.