Let's try it out on some well-known examples.
Star Trek (original series), you have Kirk as Leader, Spock makes an excellent Mystic, with McCoy as Clown. No obvious warrior, Kirk sort of inherits the rolé by default. And the rest of the cast just get relegated to backdrop.
How about Next Gen? Picard, as the captain, makes the obvious leader. Worf (or Yar) fills the warrior slot admirably (although he has some intriguing Mystic tendencies). Data gets to be the Clown. And Troi is the Mystic. A reasonably good fit (unless you're Riker or Crusher).
How about The Dark Knight. Batman is an obvious Warrior, and the Joker is the obvious Clown. That leaves Leader (Dent? Gordon?) and Mystic (Fox?) to deal with. Hmmm.
Let's do our house! I'll make myself the Leader. Then fizzygeek can be the Warrior, which works. Sammy (the siamese) is the mystic, and Callie (the calico) is the clown. That pretty much works.
How about Family Guy? Hmmm. I guess Peter can be the Leader, and Stewie the Warrior? No good match for Mystic, and everybody's the Clown.
American Dad? Okay, Roger (the alien) is the Clown here. Haley is as close as we have to a Mystic. Stan fits the Warrior mold. But there's no apparent Leader.
How about the Sarah Conner Chronicles? Sarah is the Leader. And Kyle is the Warrior. Cameron makes a decent Mystic, and a good Clown too. The emo John just doesn't stack up. Oh well.
How about that wonderful show The Middleman? The Middleman is the Leader, and Ida (with her Heydar) is the Mystic. Or is the Middleman the Warrior? Dubbie makes a good Warrior too. And Sensei Ping might be a Mystic. So could Noser, and his encyclopædic knowledge of music. Clowns abound; if I had to pick one in particular, it might be the Interrodroid.
How about the Simpsons? Homer makes a good Clown, and Lisa a servicable Mystic. Marge can the the Leader. But there isn't an obvious Warrior to be seen.
Peanuts? Lucy comes across as a Warrior type, and Charlie Brown seems like a Mystic. For Clown, there are several possibilities: Snoopy, Pig-Pen, Woodstock? Again, no apparent Leader. In fact, Lucy is the only one that seems a good fit.
Married With Children? Al is a reluctant Warrior, and Bud is sort of a Clown. Actually, they're all Clowns. Next!
How about Futurama? The Professor is in charge, so he's the putative Leader. Leela is cut from Warrior cloth. Fry is a Clown (so is Bender, really, and Amy). Several characters have a Mystic bent, the Professor again, Zoidberg, even Leela.
Mythbusters? Jamie is the Mystic, and probably also the Leader, and Adam is the Clown. Tory is the Warrior type.
Dirty Jobs? Mike is the Leader, the Mystic, the Warrior, and the Clown. Except when Dave or Doug steps into the Clown role.
Coupling? Jeff is an obvious Clown. Susan and Jane both seem Warrior material. Actually all the girls do. There's no obvious Leader, though Steve has the bearing, he's a bit of a wimp. Jane and Sally have the strength for it. Patrick, well, he's another Clown. Maybe Patrick is the Clown, and Jeff (with his bizarre view of reality) is the Mystic. Thinking on it, the girls are the real strength of the series. Were it not for their continuing interest in the guys, it would nicely meet the Bechdel rule.
How about the Six Million Dollar Man? Steve Austin (Lee Majors) gets to be the Warrior. Oscar Goldman (Richard Anderson) is the Leader. Rudy Wells is the Mystic. We seem to be short a Clown.
Star Wars? Obi-Wan is the Mystic. Luke is the Warrior. C3PO seems to be the Clown. Han is the, um, Mercenary. Oh dear.
I'm sure I've left out many peoples' pet entertainments, feel free to put them in as comments (the Beatles are a perennial favourite for this game). And tell me how I'm deeply wrong on the above!