As you pointed out, Jesse, a major reason for this sort of number-disagreement in educated writing is the reticence to use the word "he" or "him" as the neuter (in order to avoid sexism), coupled with the terrible awkwardness of "he or she" or "him or her." You also correctly point out that some readers, perhaps many, are put off and "distracted" by number-disagreement.

However, I want to point out that one accepted solution to the "male pronoun as the neuter" is to use the female pronoun instead. For example, "When a judge writes an opinion, she..." But this solution, which is both anti-sexist and acceptable to "conservative" readers, actually makes for distracting reading for many people. When I'm reading along and come across sentences like those, it's momentarily unsettling - because it disrupts the default mental state of assuming that anyone mentioned in prose who is not obviously female is male. The fact that this is the default mental state for me is unfortunate, and is indicative of our sexist cultural past (and, hopefully to a lesser extent, present). But I know it's like that for many other people too; otherwise the following children's riddle wouldn't work:

A father and his son get into a terrible car accident. They are taken to separate rooms of the hospital. The doctor in charge of the boy looks at him and says, "I can't operate. He's my son." How is this possible? Answer: The doctor is the boy's mother.

My point is that there are problems with all of the possibilities for the neuter. The male neuter is sexist; using the female neuter or switching between the male and female neuter can be confusing and distracting; saying "he or she" is awkward; and using "they" or "their" causes number-disagreement.

I happen to alternate between the male and female neuter in my own writing, because I understand that number-disagreement is unacceptable to many readers, including most of the important ones (e.g., judges, lawyers, professors). But I'm trying to suggest not that we should have number-disagreement in our writing (because that's distracting), but rather that the pronoun "they" is steadily gaining a secondary grammatical identity in which its grammatical number is one, in constructions like those we've been discussing. Writing lags behind oral linguistic innovation, as you say, but in this case the oral innovation happened long ago and my impression is that it is close to becoming acceptable in writing, as well. This is what I was soliciting agreement or disagreement on (to appropriately end this post with a sentence ending in a preposition).

-- MichaelBerkovits - 19 May 2008