The Innocence Project at Yeshiva University and other programs use DNA evidence to exonerate people wrongfully convicted of crimes. According to the Innocence Project website, the common causes of wrongful convictions include eyewitness misidentification, improper forensic science, false confessions, government misconduct, unreliable informants or snitches, and bad lawyering. Details about these causes and a geographic distribution for each cause within the United States can also be found on the website.
If DNA exoneration is a key point in your plot, you may want to peruse the U.S. Department of Justice’s report, “Post-Conviction DNA Testing and Wrongful Conviction.” It was published in June 2012, and it’s available from the National Institute of Justice website.