In general I am in favour of the use of they forms with singular reference as a means of avoiding reference to the gender of the subject, which may indeed be unknown, but they must be used with some sensitivity for context and meaning and should not lead to the double-take that I at least did on reading this:
One viewer complained to the BBC about the episode, broadcast on BBC Two in March. The BBC's Editorial Complaints Unit agreed with their comments.
What’s wrong with:
One viewer complained to the BBC about the episode, broadcast on BBC Two in March. The BBC's Editorial Complaints Unit agreed with that viewer’s comments.
or indeed with the appropriate use of his or her?
I see two problems here. One is the distance separating the One from the their. The other is the most definitely singular nature of the subject. In a more general case, for example:
A viewer who complains to the BBC can be sure that their complaint will be treated seriously.
it is clear that the singular subject is in fact being used to mean All viewers and so the inherently plural nature of the their makes a little more sense.