Like Professor John McWhorter , I have electronic access to the Oxford English Dictionary--did he really expect anyone to believe that he keeps Middle English verse romances at his bedside?--and
a handy Shakespeare concordance lying around Wikipedia (cf. Shakespeare, Thackeray, William Strunk). Unlike Dr. McWhorter, however, I've actually read Vanity Fair and thus am able to point out that, in his recent screed about pronouns over at the New Republic, the example he quotes from Thackeray is actually a piece of dialogue. This should have been clear to him if not after reading the OED (where it is not mentioned) then certainly after reading the "singular they" Wikipedia page. The same goes for the distinction between what is going on in the Comedy of Errors quote versus the solecism in his first sentence, i.e., between generic and epicene forms of singular they/them/their.
Anyway, saying that Thackeray is endorsing the singular "their" simply because one of his minor characters makes use of it is like arguing that Mark Twain was presenting "gwine" as a reasonable alternative to "going" when he put it in the mouth of Jim.
Update: I entered this yesterday as a draft, and it went up today without my looking it over. I apologize for getting John McWhorter's name wrong.