Without writing half a dozen episodes, I find it an uphill battle to tell a) If they're working and b) If they're not, what's missing. The only thing to do is to 'feel it' - to play with the characters over and over in my head and judge it by instinct.
'Feeling it' I believe to be a vital part of creating - but I also find it can be the most untrustworthy. I try whenever possible to partner it with some kind of flexible rule, tick list, or template to fall back on. For me, that is why I find 'rules of thumb' important - it's about balancing the right side of the brain with the left, and creativity with structure.
In some ways, I picture writing like journeying through a dark cave, feeling your way by instinct and talent, and navigating through a knowledge of structure and formula. I find having rules of thumb to be like having emergency flares, able to light a small bit of the cave and make sure I'm on the right track.
While balancing a cast's personalities, instinctually I could outline some vague ideas about contrast, overlap and conflict but for this post, I thought I'd copy down the only solid light source I have for balancing personalities: The Reactionary Device.
Let me give you some examples of a Reactionary Device from a kid's show we're writing:
Character #1 is monumentally stupid but also sweet, naive and child-like.
That's his personality.
He is always eager to help, but he usually makes things worse - often by helping the wrong side.
That's his Reactionary Device. It's a reaction I can use in most situations if I need it.
Character #2 is boring, grouchy and safety conscious.
That's his personality.
If something doesn't make sense he'll complain about it, ignore it, or try and fix it.
That's his Reactionary Device. Very useful in a world based on silly cartoon rules as I can use it to both drive him towards something, or drive him away from something.
Now imagine all your main characters are in a situation not unlikely in your idea: They've just found out one of them is a traitor, or a Doctor has just told them someone died, or even a genie has just given them one wish each.A character without a Reactionary Device would act very predictable, either being suspicious of the others being the traitor, or reacting with shock at the death, or simply making a wish. I believe a cast of characters that all react the same way to an event is not only boring to watch, it's hard to write. Once or twice while I've been writing a scene and I need to get my characters from A to B, I'll realise that none of them would push the others to 'B' because I had no Reactionary Devices to exploit.
Now obviously not everyone can react unpredictably to everything, that would be insanely hard to create and be very strange to watch but in every situation I aim to have at least one person act interestingly.
The Cat's crippling narcissism, Toby Zeigler's love of debating, or even Marty McFly's inability to cope with being called yellow are all excellent Reactionary Devices because they allow the writer to 'control' the character.
Arrested Development is one of the best study cases for this. Every time something happens, one or more of them will react in a plot altering way, be it the mother's need to manipulate, or Buster's need to prove himself or even Michael's need to fix everything. Imagine if the characters from Arrested Development found out one of them is a traitor, or if a Doctor told them someone died, or even if they all got a wish.
They almost write themselves.
EDIT: I came across this old Homestar Runner cartoon: 'Homestar's Pumpkin Carve-Nival' - what it does well is illustrate how having a well defined, non-overlapping cast writes itself.
If you had to write a scene/short/episode where all your characters carved pumpkins, would your characters alone give you enough material?