I think the major problem here is that women were clamoring for “strong female characters,” and male writers misunderstood. They thought the feminists meant [Strong Female] Characters. The feminists meant [Strong Characters], Female.
So the feminists shouldn’t have said “we want more strong female characters.” They should have said “we want more WEAK female characters.” Not “weak” meaning “Damsel in Distress.” “Weak” meaning “flawed.”
Good characters, male or female, have goals, and they have flaws. Any character without flaws will be a cardboard cutout. Perhaps a sexy cardboard cutout, but two-dimensional nonetheless. And no, “Always goes for douchebags instead of the Nice Guy” (the flaw of Megan Fox’s character in Transformers) is not a real flaw. Men think women have that flaw, but most women avoid “Nice Guys” because they just aren’t that nice. So that doesn’t count.
So what flaws can female characters have? Uh, I don’t know. How about the same flaws a male character would have?