Based on my (admittedly fuzzy) memory of a show I saw on Discovery Health about Chimerism, one common manifestation is to have your blood and your skin reveal different DNA.  Thereby making it impossible to (for example) match DNA from blood at a crime scene to DNA from hair/skin cells left behind at the same crime scene.
Another apparently less common but not rare manifestation is to have different DNA in blood versus reproductive cells.  I distinctly remember the show discussing a mother who had to fight the court systems for custody of her infant, because DNA from blood tests showed that she was not the biological mother, even though she was.
I found it to be a very intriguing show. I think you would have enjoyed it too.  :)