The pencil Abed uses changes repeatedly.
In season 1's Introduction to Statistics (2009) Shirley described the woman Andre left her for as a "Long neck, weave-wearing bank teller." In a later episode from the same season, Beginner Pottery (2010) her occupation would be retconned as a stripper. In this episode her appearance does not match the description Shirley gave.
In season 1's Romantic Expressionism (2010) Troy mentions that Annie had a nervous breakdown and ran through a glass door screaming "Everyone is a robot!" In the flashback she does have the nervous breakdown and runs through a glass door, but doesn't scream, "Everyone is a robot!" She does, however, say Troy is a robot, in reference to his former jock-like attitude.
In Pilot (2009) Annie stated that Troy injured himself in a keg stand dislocating both shoulders in the process. Troy only corrects her by saying it was a keg flip. In this episode, Troy is shown doing the keg flip but injures his knee instead. Community writer and executive producer Andy Bobrow acknowledged the mistake on his Twitter account. Also, in season 1's Football, Feminism and You (2009) Troy mentions that he injured himself on purpose that night. In this episode, however, his injury turns out to be fake to begin with.
In Season 2's "Intro to Political Science" (2011) it's revealed that Magnitude is (according to his character card on Troy and Abed's news segment) 16 years old. During the flashback of Annie running through the glass door at the party (2008), it wouldn't make sense for Magnitude to have been there, as he was only a 13 year old.
Abed makes a reference to the Star Wars prequels being terrible, and that Chewbacca should have remembered Yoda, but in the original trilogy Yoda only meets Luke on screen, Yoda never leaving his planet in the Dagobah system.