Other mistake: In the scene with the swimming pool full of mud and the kids playing on it, the sign on the entrance is supposed to be in Spanish, but most of the words are misspelled and no sentences make sense.
Factual error: At the end when Kate Winslet receives the Fed Ex box she opens it easily from the end. Fed Ex boxes have pull tabs that you pull to open, and if you decide you want to open the box at the end it is not as easy as she made it look.
Answer: I believe that she was a plot device to make sure David Gale had nothing to lose by the end of the movie. She then may have felt guilty about casual sex, and tried to get back at Gale. She then later felt guilty about the whole charade, and wrote him a postcard admitting what she had done. Then the postcard is given to the ex-wife to show he was innocent of rape.
Richard Welty
David had asked Bitsy and, presumably, Dusty, to preserve his son's memory of him. So they/he/she forwarded the postcard from Berlin so his ex would know he was innocent of the rape charge. Along with money for his son.