This word is considered to be a plural possessive pronoun, but it has been used in the singular sense since the 14th century, especially by such notable writers as Shakespeare, Chaucer & Spenser. Even the King James Bible uses it and so does the Oxford English Dictionary. However, from the late 18th century onwards, pedantic grammarians started to complain about this usage, although this didn't stop Jane Austen sprinkling it all over her novels. Not just in characterisation, either. She also uses it in narration, which suggests that she herself used it in speech.
(from Jesus Christ Superstar)
Other well-known writers who have used the singular "their" are: Jonathan Swift, Daniel Defoe, Frances Sheridan, Oliver Goldsmith, Henry Fielding, Maria Edgeworth, Percy Shelley, Lord Byron, William Makepeace Thackeray, Sir Walter Scott, George Eliot [Mary Anne Evans], Charles Dickens, Mrs. Gaskell, Anthony Trollope, John Ruskin, Robert Louis Stevenson, Walt Whitman, George Bernard Shaw, Lewis Carroll, Oscar Wilde, Rudyard Kipling, H. G. Wells, F. Scott Fitzgerald, Edith Wharton, W. H. Auden, Lord Dunsany, George Orwell, and C. S. Lewis. Quite a few well-respected names in that list!
The simple fact is, there is absolutely nothing wrong with using "their" in the singular sense. The reason the 18th/19th century grammarians complained about it was based on a kind of pseudo-logic deduced from Latin which in actual fact has nothing whatsoever to do with English. The alternative, which is what was used before the late 1300's, would be the word "his", as in "Everybody loves his own mother" as opposed to "Everyone loves their mother". Totally ignoring the sexist flavour of the former, the latter is far easier to say and far less cumbersome to hear.
In conclusion, therefore, I would say that when it comes to the use of the singular "their", everyone is entitled to their own opinion.
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