I was watching A Bit of Fry and Laurie the other night, and as much as I enjoy it, it strikes me as the kind of show that could only be make in England, and is only accessible to a certain kind of audience. The range of jokes in a single episode, from faked and exceedingly funny cultural criticism, to satire of pretentious businessmen, to dead-on knock-offs of Australian soap operas, requires a broad and particular kind of cultural literacy.
Obviously, cultural literacy in the E.D. Hirsch Jr. sense is not unproblematic. Attempts to draw up a clear catalogue of what all Americans, or all educated people, or whatever dividing line one chooses to set, ought to know will inevitably exclude some set of knowledge, will inevitably result in some sort of difficult and tippy balance. Do we include comprehensive knowledge of hip-hop but leave out Native American traditions? Do we include English history and leave out pre-Colonial Africa? There's no way to create a canon that includes deep knowledge of a fairly broad range of subjects without leaving anything critical out.
And yet, having some knowledge in common is such a gift to comedians. If you can assume your audience knows certain things reasonably well, you can use that knowledge, build on it, rely upon it, riff on it. The comedy of inference is available to you, and not simply the inference of family dynamics or behavior, but the inferences based on culture, history, custom. A show like Community does extremely well within the realm of popular culture, but I can't really imagine an American show that's as broad and rich as British sketch comedies like Fry and Laurie seem to be.