Problem #1: Training only with other women.
There's absolutely nothing wrong with training in a women's only class here and there. One big pro is the absence of the stereotypical male ego, and the fact that many gender-specific issues can be more fully explored with the absence of men. The biggest problem lies in what I call "preparation for the field:" in a real self-defense application, statistics show that women are more likely to be attacked by male perpetrators than female ones. Of course there will be "girl fights" to be had, but it makes sense to be prepared for the most likely scenario as well.
Problem #2: Being too passive
We can blame society for this one. Even in today's "independent woman" society, from the day they're born, the majority of women get messages every day on how a woman "should" be: submissive, docile, feminine, "sugar & spice and everything nice," nurturing, etc. I realize how sexist this sounds, but that's the message conveyed on TV, magazines, and so forth. Many of those same "feminine" traits are what dooms many women in a self-defense situation.
Problem #3: Misunderstanding the ugly truth of self-defense
This is a big problem with men as well, but more so with women simply because of how the two sexes are raised (see Problem #2). Seeing women cringe at the fact that at some point they may have to scratch and claw at someone's eyes, throat and/or groin to save their lives further illustrates this point. Self-defense affairs are ugly, and the sooner this point is understood, the better.
Problem #4: Being too concerned about the other person
This one is most prominent when it comes to sparring, and typically when women spar each other. Out of concern for safety (nothing's wrong with that by the way) women tend to check on each other after one hits the other ("Are you ok?!?! I didn't mean to hurt you!!!). What this is doing is setting up false pretenses for both parties, as on the street, it may be necessary to hit, hit and hit again (as opposed to hitting once) and to frankly not care if the assailant is hurt or not. In class, of course safety comes first, but the habit of hitting a person and stopping to check on them (unless they're truly hurt) creates a bad habit that can be hard to break.
Problem #5: Expecting chivalry in the dojo
Also a problem for men as well, many women don't expect to be hit hard (or at all in some cases). Regardless of whatever reason a person begins taking martial arts classes, self-defense is still the primary focus. It is totally unrealistic to expect a rapist or mugger to not hit you, right? Yes, everyone (men included, even though many won't actually admit it) has at least an initial fear of being hit. The only way to get over that is to mix it up in class in order to prepare you for the street.