I am with Kevin Drum. I got tired of using "his or her" or some other such kluge some time back. I am using "their" until someone defines a better third person possessive pronoun that is gender-neutral (ditto "them" for "him or her"). After all, unlike French, English is a bottom-up language defined by common use rather than unchanging top-down rules. So if enough of us use "their", it will become correct.
For those of you too young to remember, the invention of "Ms." as a generic women's prefix was one of the greatest improvements in the English language in my lifetime. If you despair sometimes in looking down a list of names and trying to guess if the person is a "Mr." or "Ms." (remember "Pat" on Saturday Night Live), you wouldn't believe what a pain in the rear it was to figure out if one should use "Miss" or "Mrs." for a given female.