The political correctness movement has instigated many changes---not always good ones---in the English language. One problem that has yet to be resolved satisfactorily, however, is the unavoidability of specifying gender when it is unnecessary or even inappropriate. An example is the following: what possessive adjective goes with the gender-neutral pronoun "someone"?
I once had a writing teacher at Harvard who insisted that we use "their," despite that being grammatically incorrect; for that feminist, apparently the lack of numerical agreement was less of a sin than making assumptions about the sex of the subject. Now, I consider myself quite a feminist as well---I despise the title "Mrs.", and I've certainly fought my share of battles proving that women can do math and science---but I am also a grammarian, and this just bugs me. By this logic, would one also have to say, "Someone didn't clean up after themself?" How can multiple people have one self? Or do you say "Someone didn't clean up after themselves?" Now one person has multiple selves. Either way, it's inconsistent and grating.
Another phenomenon I've seen is the invention of unisex adjectives like "hir." Perhaps if it gained wider usage it might look less ridiculous, but I don't see that happening. In the meantime, it sticks out even worse than the gramatically incorrect "their."
My practice is to use the somewhat cumbersome "his or her" when it doesn't over-complicate the sentence, and when it does, to pick one gender and use it. It doesn't always have to be the male "his" or "himself", and in fact it's nice to reverse the expected choice once in a while and use "her" for a doctor or boss. I've read books and articles on parenting where the assumed gender of the child is changed every paragraph or section, and as long as it is done in a way that doesn't disturb the continuity of the prose, it's great.
How about other languages? It's interesting to me that Spanish has the gender-inspecific possessive adjective su, although the vocabulary in general makes many more distinctions by gender; a doctor is a médico or médica, for example. Mandarin Chinese has the convenient pronoun tā, which can mean "he" or "she". And then there is Hebrew, which has the gender of the speaker built into the conjugation of the verb itself so you can't possibly escape it.
The constructors of Esperanto were apparently conscious of this issue too, as they recommend ĝi ("it") as a gender-inspecific pronoun. This could be a neat solution for the problem in English, except that some people seem to have an aversion to sharing a pronoun with inanimate objects. In fact, English speakers of Esperanto have proposed a pronoun ri that is separate from li ("he") and ŝi ("she") reserved for humans. This seems like an unnecessarily complicated solution to me, but as I've already expressed lack of interest in learning Esperanto (see this previous post), I'll refrain from further comment.