"Neither the highest scorer nor the lowest scorer in the group had any doubt about their competence."
Example from Wikipedia. The usage isn't correct according to a few style guides, which means I should have caught it before the article was submitted - if I had been paying attention, of course.

"Neither the highest scorer nor the lowest scorer in the group had any doubt about his or her competence."
It's a little more clunky, yes, but the other usage is not grammatically correct even though it's common. Time for me to break out my old Elements of Style book, eh? Anyone else want to share their mistakes?
CJ, over and out