Answered by Susan, Hiring Expert at Praxair, Inc., on Monday, August 26, 2013
Good question. Depends on what part you got wrong, perhaps. If it's a minor mis-spelling of their name, I would likely not follow back up. However if you had the wrong name with someone else's title, then yes I would follow up (but make it very brief!) indicating you recognized your error, are correcting it and hope (s)he will view this as an indication of "acknowledging mistakes and rectifying them".