A common criticism is that (allegedly) strong female characters are one-dimensional.
Oft-cited problems with strong female characers include:Edit
her strength is in martial arts, but she has no strength of character
she still has to conform to gender-normative standards of attractiveness
she will wear skimpy or fetishistic gear to fight in
she will be strong right up until she can't deal with something and has to be saved by a man
her strength is diminished when she gets interested in a member of the opposite sex
her strength is primarily a narrative tool to measure a male protagonists' progress in his emotional maturity plot arc, in which his full maturation is signaled by getting the girl, and her interior life or own motivations are not portrayed (such female characters often feature in works that fail the Bechdel test)
"You know what's a problem? Strong female characters. First of all, why do we have to specify "strong" when referring to "female characters?" Why is this not a given? The default for male is not "strong" or "wusstastic," so why do we have to be so specific about the chicks?"From Hark a Vagrant by Kate Beaton
Hark a Vagrant comic - Strong Female Characters by Kate Beaton. Created together with Carly Monardo, Meredith Gran - The comic parodies the popular treatment of female characters in American comics. Beaton highlights the practice of giving characters a veneer of physical strength or skill, which is seen to somehow mitigate otherwise highly sexualized and stereotypical traits.