Is there even one death penalty execution where the DNA shows that a mistake has been made?

Despite the concerns about possible errors in the death penalty and the use of DNA evidence, one thing is very clear: there is not a single case where DNA shows that an innocent person was put to death.  From the Crime Prevention Research Center:

The one modern case that death penalty opponents point to that comes closest to meeting this claim involves Claude Jones Texas, who was convicted in 1989 and executed in 2000. Two pieces of evidence were involved in his trial: the testimony of two accomplice who planned the robbery with Jones and who provided him with the gun used in the killing as well as a hair sample at the scene that turned out to be someone else’s. The fact that the hair at the scene was someone else’s would have meant that piece of evidence could no longer be used to prove that Jones actually went into the store, but the failure of the DNA test to match Jones to the hair does not prove that Jones didn’t do the killing because some many people visited the store it could have been from someone who didn’t commit the murder. The issue here is whether there was still enough evidence with the witness’ testimony and the gun to place Jones at the scene of the crime. . . .

The CPRC has useful discussion on the over all error rate for death penalty cases available here.