About a year ago, I asked whether any false convictions have resulted from DNA database searches.  Of course, if there are any, they might be hard to find, but there is a known recent case of a false initial accusation. It came about because a laboratory contaminated a crime-scene sample with DNA from an whose DNA was on file from other cases.
In March 2012, a private firm in England re-used a “plastic tray as part of the robotic DNA extraction process.”  The tray, which should have been disposed of, apparently contained some DNA from Adam Scott, a young man from Exeter, in Devon.  This DNA contaminated the sample from the clothing of a woman who had been raped in a park in Manchester. Police charged Scott, who claimed he had never been to Manchester, with the rape. After detectives realized that Scott “was in prison 300 miles away, awaiting trial on other unrelated offences” at the time of the rape, the charges were dropped.  An audit and investigation of 26,000 other samples analyzed after the robotic system had been introduced, uncovered no other instances of contamination. Steps intended to prevent a repetition of the error have been implemented. 
Other errors in handling samples have been documented. In a 2001 Las Vegas case, police obtained DNA samples from two young suspects, Dwayne Jackson and his cousin, Howard Grissom. A technician put Jackson’s sample in a vial marked as Grissom’s, and vice versa. A falsely accused Jackson then pleaded guilty and was imprisoned for four years. The error came to light in 2010, after Grissom was convicted of robbing and stabbing a woman in Southern California. California officials took Grissom’s DNA and entered the profile into the national database, leading to a match to the crime-scene DNA from the 2001 burglary for which Jackson had been falsely convicted. 
Of course, this is not a case of a DNA database hit producing a conviction or even a false accusation. Quite the contrary, it is a case of a DNA database producing an exoneration that would not have occurred otherwise. But both cases vividly illustrate the need to implement quality control systems that reduce the chance of handling and other error and to avoid over-reliance on cold hits.
Addendum of July 10, 2012: If anyone has trouble posting comments, please email me. Jeremy Gans ran into problems trying to post an excellent and informative comment that I am posting on his behalf.
1. David H. Kaye, Genetic Justice: Potential and Real, The Double Helix Law Blog, June 5, 2011.
2. BBC News, DNA Blunder: Man Accused of Rape After Human Error, Mar. 21, 2012.
3. Simon Israel, DNA Contamination Blamed on Human Error, Channel 4 News, May 9, 2012,.
4. Lawrence Mower & Doug McMurdo, Las Vegas Police Reveal DNA Error Put Wrong Man in Prison, Las Vegas Rev..-J., July 8, 2011.