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.
Defictionalization: Screener DVDs were packaged with cootie catchers based on the opening credits sequence.
In the second episode to feature Abed's father, "Basic Genealogy":
Jeff:(in tears) We always used to watch the shows she wanted to watch... I hate Glee. Pierce:(beginning to tear up too) Yeah, I'm not fond of Glee... Jeff:(sobs) I hate it...* sniff* ... I don't understand the appeal at all!
There's as much poking fun as there is sniping. Previews for the premier of season two depicted Betty White confused as to whether she was guest starring in either Community or Glee.
In "Modern Warfare" Jeff tells the Greendale Glee Club to "write some original songs!", then in "Paradigms of Human Memory" we learn that their Glee Club died in a bus crash.
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 Harmon was forced by NBC execs to hire females for half of his writing staff. He ended up appreciating their skill and kept hiring a large number of females 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, "I’m not saying you can’t make a good version of Community without me, but I am definitely saying that you can’t 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.
The accounting teacher/debate coach is Wayne Jarvis!
Donald Glover (Troy) is from moderately well known online comedy troupe Derrickcomedy, creators of such YouTube classics as "Bro Rape" and "Niggerfaggot" "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 Gambino*
"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?
In "Beginner Pottery", some of the study group takes a pottery class taught by Buster Bluth while the others take a sailing class taught by Steve Austin.
Apparently Nurse Rose has a thing for guys with impossibly good hair, and a pattern of getting ditched for other women and disappearing forever. Sorry, Professor Slater.
Two of the stoner set are Morgan Grimes and Badger. Well, at least they're in college...
This film answers the question of what would have happened to Rhoda on Earth 2 - she would have gone to community college instead of MIT, and not been a lesbian.
"Custody Law and Eastern European Diplomacy" has Enver Gjokaj as Lukka, again showing his affinity for accents.