Can You Use 'They' and 'Their' for a Singular Subject

A lot of people object when you use a plural "they" or "their" to refer to a singular subject, as in "Every visitor should be sure they lock their car." But is it wrong?

[audio:http://www.grammarunderground.com/wp-content/uploads/2011/05/0046-They-and-Their-in-Reference-to-a-Singular-Subject-mp3.mp3|titles=0046 They and Their in Reference to a Singular Subject mp3]

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