But, the big problem with the show, is that the drama sucks. That isn't really a problem, because it's a comedy. The problem is that shows like this, comedies, need relationship, it's the thing that keeps it together. The stickiness.
Look at the best comedies, they all have a bit of drama. The Simpsons definitely has it (or had it). Homer got his job after almost committing suicide for failing his family; Marge and Homer have separated countless times; Bart sings to Lisa on her birthday; Homer saves Barney. Seinfeld has Jerry and Elaine, plus all of the characters had good relationships with each other. Family guy has it, The Office beats it to death (and notice now that the Pam and Jim thing is done, the show suffers), and Arrested Development rocked it with every character.
There is only one good show I can think of that doesn't really have any relationship, Southpark. Maybe I'm wrong, I don't remember the show that well, but I can't pinpoint any real relationship in that show. So how do they work as a show? Zany. Non-stop zany. They can make episodes lightning fast and can just pick anything in the news and rip it to shreds. Pick a subject, make non-stop jokes without limit, end episode. The show is pretty much a 22 minute long Conan opening with cartoon characters.
And that's what Community is doing. Non-stop jokes for the episode, delivered perfectly, with awesome themes. But no relationship. They tried the Britta/Jeff thing, they tried the love-triangle, they tried the sad Pierce, the sad Shirley etc. They all failed. And they know it, it's why they dropped all of those story lines. Their writers know this, so they keep trying different angles of drama (which is predicated on relationships) and they keep failing. They have moved on to moves that are reserved for season 6 or 7. Self-referencing, calling out characters on their classic moves, call-backs to past episodes. They succeed at the zany, but it's not sustainable. They can't do it like Southpark. Southpark picks from whatever is hot and kills it. Community can't do that. They do genres and character jokes, and they will eventually run out. Thus they will fail. So soak it up while you can; there will not be another show like it.
*Note: Donal Glover wrote for 30 rock, does great stand up http://comedians.jokes.com/donald-glover, and is the oddly serious rapper Childish Gambino. Give him 6 months.