Can't find the secret objectives documented anywhere. I don't own the game (only played it once) but it seems like a player who gets a betrayer card would be harder to uncover if he knew what other objectives he could be faking. I assume you can't simply ask a player what their objective is (right?), but some are probably easier to fake than others. For instance, there's one for having four or more survivors (name escapes me), which is a good one to fake if you think you can manipulate other players into helping you amass them.
Most players that I play with regularly wouldn't want to know the other objectives. It makes the game much more fun and tense to guess at people's motivations rather than thinking, "Oh, he needs three fuel cards because he has objective X."
I find that if a player is super-helpful in Round 1 and gradually backs off from contributing, that is a much better indication of being a Betrayer than knowing a few of the objectives and what she might be playing for. Also, several Betrayal! objectives and normal objectives overlap, certainly intentionally, so you might focus on the wrong person for the "right" reason.