(or "Failure Is Funny")
I don't think it'd be controversial to say that Jim Henson was something of a genius when it came to comedy (then again, judging by some of my previous posts, I also don't think it'd be controversial to say that I'm not good at guessing what's going to be controversial and what isn't.) He certainly spent time thinking about settings and character dynamics that would help him come up with skits for a half-hour variety show; he's famously quoted for his axiom on how to end a comedy sketch ("blow something up, have one character eat another, or start tossing animals in the air"), but he also spent a lot of time working on ways to begin one. 'The Muppet Show', his best-known series, is filled with recurring gags and repeated characters that somehow never get old, and it all comes from one of the simplest rules of comedy. Failure is funny.
Well, let's clarify that a bit. Other people's failure is funny, so long as you don't focus too sharply on the consequences of that failure. 'Requiem for a Dream', for example, is never going to be regarded as a comedy classic. But looking at the Muppets, you see a group of people united by a) their passion for entertainment and their dream of making people happy through art, and b) their lack of talent at their chosen field. The gap between their desires and their actual abilities provides fertile ground for chaos, confusion, and comic misunderstandings as events slowly (and sometimes quickly) spin out of their control.
It starts with Kermit, who's the emcee and showrunner, but who has problems controlling his temper and asserting his authority. Not only can he not keep his cool when problems hit, but when he does fly into a rage, it's endearingly cute instead of intimidating. Then we have Fozzie, who's almost the perfect emblem of the show; he's a comedian who's so unfunny it's funny. Miss Piggy is a diva who doesn't conform to the traditional feminine standards of beauty, but who acts like she does. Gonzo is an avant-garde performance artist trapped in a run-down vaudeville theater, Bunsen Honeydew's inventions don't work, Sam the Eagle continually fails at injecting moral uplift into the show, Wayne and Wanda can't ever finish a single song, Statler and Waldorf are continually disappointed in their hopes of seeing quality entertainment--really, the only characters who seem fulfilled are Doctor Teeth and the Electric Mayhem, and you still get the feeling they'd rather be doing arena rock for a bunch of counter-culture types.
This "comic disaster" mentality permeates every aspect of the show, helping to create not just sketches but entire episodes that are structured around a slowly building crisis--Carol Burnett, for example, comes on the show to do her "classic" comedy bit, the "lonely asparagus" sketch. But due to a scheduling conflict (Gonzo's running a dance marathon in the theater that week), all her efforts to get some stage time are continually frustrated until at the end, she only manages to get off one joke before time runs out and the show's over. Quite clearly, they only had one joke they could come up with in the "lonely asparagus" sketch (it's too terrible to repeat, even by my pun-happy standards), but by turning the story into the failure of the sketch, they made that one terrible joke into an entire hilarious episode.
This structure also allows Henson to come up with recurring characters and sketches that nonetheless manage to be funny every time, despite only slight variations; somehow, seeing incompetence never manages to become too formulaic, no matter how many times we see it repeated. The basic gag for the Swedish Chef is the same every time, but it's always funny to see an incomprehensible guy fail spectacularly at a simple task. In fact, the Swedish Chef is probably the perfect distillation of the entire concept of the Muppet Show (and 'The Jim Henson Hour', and 'Muppets Tonight', and all of the various movies and specials and, well, everything else Muppety.) Watch the Swedish Chef, and you'll understand Jim Henson's genius in less than two minutes. He wants to teach people how to cook, but he can neither cook nor teach. That's just always going to be a good start to a comedy bit.