Audio problem: When Constance informs David that he has been put on official "sabbatical" and unofficially released (as a professor), she adds vocally that the vote was "4-2". However, her lips do not move, and the exact vote turnout sounds distorted, because it was edited later.
Audio problem: When Bitsy and Zach arrive at the motel Zach gets out of the car and we hear his door close normally. When Bitsy gets out she visibly slams the door, yet there is no sound.
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.