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Why doesn't Dakota tell the cops to call the strip club where she works to confirm her identity? Since she is Aubrey's twin, that means she is underage, therefore the club owner would most likely go along with the "That woman's crazy" theory if the police interrogated her.
Better yet, the police could have checked to see if a woman named Virginia Sue Moss died around the time Dakota said she did, or could have checked out Dakota's apartment. But that would be too easy.
How about: 1. Nobody in the hospital told Susan her baby had died. 2. Nobody in the hospital noticed that the family whose baby died left the hospital with a baby. 3. Nobody in the hospital noticed that Virginia Sue Moss was missing a twin.