Language is both a means for communication, and art. As such, I think grammar nazism is uncalled for when it's obvious that the writer is capable and knows what he/she is doing. Actually, in the above sentence, I'll often use 'they' instead of 'he/she', although I know it is incorrect. Personally, I think we should extend 'they' to cover 'he/she'. A prof of mine related that he was once in a lecture by Feynman where a graduate student pointed out to Feynman that he had used α to designate two different variables in the same set of equations. To this Feynman replied: "Well, if you understand what I am talking about, it doesn't matter."
Gender-neutral pronouns are a tricky one. There are a couple of interesting proposals, including "s/he" or "ze". Extending the use of "they" is probably the most viable, although it does lack a bit of grace. I don't know if you're male or female (or something else), but I'm male and I get a unique thrill of alienation when I hear someone say, "Anyone should be able to eat ice-cream for dessert if she wants." I love it! I'm happy for speakers to use "he" or "she" as example people, so long as both are used in roughly equal measure.