The interiors of the DVD cases are designed as yearbooks, Greendale brochures and even Abed's notebook from Cooperative Calligraphy.
Among the many tidbits included are (presumably canon) hometowns for the main characters. Strangely, everyone is kinda paired off in this respect: Jeff and Shirley are from Denver, Abed and Britta from Riverside, Annie and Troy from Greendale itself, and Pierce and Chang are from out-of-state (Wyoming and California respectively).
Season 3 episode Foosball and Nocturnal Vigilantism shows shared flashbacks of Shirley and Jeff as children, and while they don't specify that it's Denver it does confirm that they grew up in the same place.
Creative Differences: Chevy Chase has frequently been vocally dismissive of the quality of the show, with numerous reports of backstage arguments about the direction of the show and his character and a notable feud with creator Dan Harmon. His decision to quit the show in November 2012 came from Chase's displeasure an Pierce's increased bigotry. He was willing to film a brief cameo appearance in the season 5 premiere, however, suggesting that the rift between himself and Harmon has been exaggerated to a degree.
Outside of praising the other members of the cast Chevy Chase rarely seems to have much in the way of praise to say about the show. In part, Chevy would appear to have issues with Pierce's ever increasing bigotry.
Several of Donald Glover's songs as Childish Gambino have lyrics that can be interpreted, if not outright stating, that he wants to leave the show.
Dan Harmon had a major backlash to season 4 when he finally watched it after being rehired to the show for the fifth season, to the point he actually apologised over it.
In a very mild example, Joel McHale has complained (Notably on the commentary track for "Advanced Introduction to Finality") that the DVDs only feature the episodes as they originally aired, rather than including extended cuts due to the number of scenes that have to be cut to meet an ever shrinking running time.
Defictionalization: Screener DVDs were packaged with cootie catchers based on the opening credits sequence.
Season 2 changes some of the focus to $#*! My Dad Says, with a sub plot about Troy's twitter account, Old White Man Says, collecting the insane rantings of Pierce with Pierce wanting to cash in on it with a sitcom. The series premiere of that show was even the same night as the season 2 premiere (which had that Troy subplot).
In part due to the focus on nerdom in general, and later being put up against each other in the same time slot, there is a certain rivalry with The Big Bang Theory. It's probably more apparently between the fandoms rather than anything else.
Another example of Tropes Are Not Bad is that originally, NBC execs demanded of Harmon that half his writing staff were women. He ended up appreciating their skill and kept hiring a large number of female writers even after the comporate rule was dropped.
Regarding implications by network brass that he'd stay on as a contractually obligated "executive consulting something or other", Harmon writes on his blog, "Iím not saying you canít make a good version of Community without me, but I am definitely saying that you canít make my version of it unless I have the option of saying 'it has to be like this or I quit' roughly 8 times a day."
Friday Night Death Slot: It was announced that Community would in fact return for a fourth season...at 8:30 PM on Fridays. Cue fandom terror. And then the show aired in it's original Thursday time slot after NBC cancelled a number of their new shows before mid-season.
Donald Glover (Troy) is from moderately well known online comedy troupe Derrickcomedy, creators of such YouTube classics as "Bro Rape" and"Spelling Bee".
For alternative hip-hop fans, it's more of a Hey, It's That Voice! - or at least it would be if Childish Gambinonote "Donald Glover" transformed by a "Wu-Tang Clan name generator" online didn't openly identify himself as Donald Glover and repeatedly reference his role as Troy in his songs. Dude can rhyme a lot harder than "donde-esta-la-biblioteca".
The rest of Derrickcomedy also cameo as a sketch group that feeds Pierce movie riff jokes in season 1.
Danny Pudi (Abed) was in several commercials before doing this show, from McDonald's snack wraps to the Blackberry "butt dialing". He has even appeared as an annoyed customer in a Walgreens training video.
Wait, how did Trudy Campbell get here? Why is she nineteen? Shouldn't she be, like, seventy? And why is she Jewish?
Oh my god, you can't just ask people why they're Jewish.
McLeaned: Chevy Chase's departure being as acrimonious as it was, this was perhaps inevitably Pierce's fate.
Money, Dear Boy: Despite the critical acclaim and passionate fanbase, Chevy Chase has been very outspoken in his disdain for the show, from calling his decision to join a "mistake", to his run-ins with eventually-ousted Dan Harmon, to criticizing sitcoms as "the lowest form of television." He's stated that the paycheck and his castmates are the only things that keep him showing up.
Chase appears to have something of a dislike of working in television in general, not just the show, although he has raised a lot of specific criticisms and complaints of the show specifically, including its perceivedly frequent Tastes Like Diabetes moments. The latter part about working with his castmates being one of the only things bringing him back is also slightly ironic in that his castmates often tend to make fun of him in very public ways (albeit often precisely because he's always dissing the show in public).
Screwed by the Network: The firing of Dan Harmon after season 3; cutting seasons 4 & 5 down to 13 episodes, so the seasons never managed to build any momentum; and the show's cancellation at the end of season 5 in the face of the long standing fan campaign for 6 seasons.
Troubled Production: Partially due to the budget cuts instated by NBC, the showrunners were scrambling to meet deadlines for their shows, with Chevy Chase saying in his Reddit AMA would lead to *sixteen to twenty hour work days*.
Greg Cromer, who played Rich, was the runner up for Jeff. Had The IT Crowd gotten picked up, he would have gotten the role since Joel McHale would have been unavailable.
The show was originally supposed to tell a self-contained story spanning four seasons with a clear beginning, middle, and end. Harmon's firing for the forth season destroyed that, so he ended up having to spend most of the fifth season resetting the status quo in order to resume the story where he left off... just in time for it to get cancelled.
In "Repilot" it is ultimately a hologram of Pierce that gets Jeff to abandon the law suit against Greendale. However, the script used at the table read instead featured the in-universe reveal that Star-Burns was alive, and he would serve the same purpose as the hologram; this was likely the plan if Chevy Chase hadn't agreed to shoot the cameo.