Is it correct to use 'they' when writing about a single, unknown person? For example: The visitor came to the front door, they knocked, but there was no answer. or Someone left their coat behind. If not, what is correct in this situation?
It's idiomatically, but not grammatically correct. You can avoid it: A visitor came to the front door and knocked. There was no answer. Someone left a coat behind.
Sorry, I should have not said it's 'correct' (though language correctness is more about communication than rules), but rather that it's perfectly acceptable based on everything I've ever seen, whether fiction or formal writing, and most people aren't grammarians, and it's not really even ever confusing unless you're the kind of person who'll stop reading a text and wonder if 'someone' did in fact leave 'their' jacket in the sense the 'their' is referring to some collective jacket that a group of people own and not referring to the 'someone' in the same sentence. heh I mean, someone left a jacket... omg, without a possessive I have no clue if it's their, sorry, his or her jacket or did they steal it? English language is so confusing! I don't see the problem, shrug.
There's a pretty interesting article on this in the NY Times from 2009. Just do a Google search for "singular they" and you'll hit it on the second link. Apparently, authors used "they" for ambiguous number and gender for hundreds of years. A book called "A New Grammar", written by Anne Fisher, appeared in 1745 and assigned "he" and "him" as the universal pronoun. Ever since then, strict grammarians have been looking down their noses at the use of "they" for an ambiguous case. Of course, in my opinion, the only reason that the debate even exists is that we distinguish humanity from everything else. We refer to an inanimate object as "it". We tend to refer to a wild animal as "it". We may refer to a pet as "he", "she", or "it", depending on our feeling toward it at the time. We always -- unless we intend to be derogatory -- refer to a human as "he", "she", or (as we've discussed) "they". We would save a lot of time and angst if we just referred to people of unspecified identity as "it". Imagine the debate THAT would cause.
Thanks for the article - I will read it. Off topic, but going on from what you said, usually a baby is called an 'it' if we are unsure of the gender (e.g. on an ultrasound, 'Ooh look, it's waving!')- when does a person become a 'them' instead of an 'it'?