Ok, I've been re-reading the Tannhauser revised rules, and realized I might have had something wrong all along... I always assumed that to make a team all the characters had to share an affiliation symbol. I thought this because the mercenary affliation symbol meant that a character could be played w/ any faction. But after re-reading the rules I realized it never said you had to share an affiliation symbol, they just had to be part of the same faction. So what I wanted to know was, besides common sense, how do I know which characters belong to which faction? Is it just by reading the Bio's on each character, or is there a more rules lawyer way of telling?
How to tell which Faction a character belongs to.....?
Well your both right and only a little wrong. The Affiliation Symbols were from Tannhauser 1.0, and they never really lived up to their potential. So, when FFG made Tann. 2.0 they kinda made them pointless and said that all characters must share a faction as opposed to a symbol.
The quick and dirty way to dertermine faction is to flip over the character card and look at the color of the back, Union is yellow, Reich is green, Matriarchy is red, and Mercenaries are brown. The colors won't be very vivid on older prints of Tannhauser.
Now, there are a few exceptions to this rule, namely Oksana and Gorgei, who can play on factions other than their own, for Oksana it's best to check her rules to get an understanding of how she is different. For Georgei he's a mercenary who can't fight against the matriarchy.
You can of course still go by Affilation Symbol, as all characters in a faction share at least one, except Oksana, she's just weird in a lot of ways.
Shared symbols:
Union: the 42 MSF sheild
Reich: the Obscura Korps roundel
Matriarchy: the Gromoviti Znaci (for most Matriarchy characters this is their only symbol)
Mercenaries: the "1" stamp
Hope this helps.
In the case of mercenary characters, it usually outright states the limitations. In fact, off the the top of my head the only characters who are universally usable are Wolf and Asteros, I think.