A wolf in sheep's clothing is someone who tries to trick you into trusting them by presenting themselves as unthreatening, then unexpectedly attacks you.
A poser is someone who pretends to have a "better" social/intellectual/economic position than they really do. @Jay's example is slightly odd (though not uncommon), in that the supposedly "rough" background is in fact considered "better" in certain social contexts (it has more "street cred"). It's an example of inverse snobbery.
It's not clear from the question exactly what kind of "good" image our subject is presenting, what kind of "bad" reality is being concealed, or why she's doing it. Either or neither of the above might apply (but probably not both).
Other possibilities are cheat, liar, deceiver, imposter, pretender, fake, faker, fraud, sham, decoy, defrauder, dodger, double-crosser, double-dealer, trickster, charlatan, two-faced [person].
Personally, I like duplicitous (deceptive in words or action) for general use. But if it's a woman pretending to be sexually modest when I know she's not, I might call her a closet sexpot (a term of my own invention here, but which I'd expect to be understood by anyone I might say it to).
I don't know of a phrase where someone can so generically point out a flaw. In your example, I'd say human - nobody is perfect. Perhaps his weakness or limitation would fit here.
There are words for dramatic flaws.
An Achilles heel: a portion, spot, area, or the like, that is especially or solely vulnerable. It does not need to lead to his downfall; it connotes someone who is pretty damned perfect except for this one thing. "Tom Cruise has an Achilles heel" would be understood that way.
His Achilles heel is his quick temper.
Shortcoming, or foible would be understood as an understatement; if he's crazy, that's a major problem; to call it a foible before stating the flaw would be mildly sarcastic.
A tragic flaw in drama is a failing of character in the hero (someone of high repute/honor/etc.) of a tragedy that brings about his downfall. Regarding Hamlet:
He has exceptional qualities like graceful personality and popularity among his country that is eminent. His tragic flaw is his delay in action and irresolution...
Other expressions for this are simply flawed, or inadequacy.
Best Answer
You can use "entitled" as an adjective; if the context is right it is implied that this refers to an unreasonable expectation of entitlement.
Here is an example of this word being used this way, found via Wordnik:
–"Chris - Seattle", September 10, 2009 at 4:23 pm, comment on "In selling health care, Obama's numbers pick may be telling", CNN