R. Williamson and R. Duncan in their Commentary (Nature 418, 585–586; 2002), recommend universal testing “as a deterrent from crime for all members of the community [that] would make the task of catching criminals easier for police”.
The obvious flaw in this proposal is the ease with which biological material can be moved from one place to another. Anyone with criminal intent could simply collect biological material (cells from a toothbrush, perhaps?) and plant the evidence at the scene of their crime. In the society proposed by Williamson and Duncan, respect for DNA evidence would be total, and thus innocent people would more easily be convicted.