>>There's a big difference between accidents occurring and the government deciding that a person should be put to death.<<
Apples and oranges. Government is not a physical thing. It is a collection of people making decisions. If someone (or group) makes a wrong decision and accidentally "decideds to kill" his own troops in war in a "friendly fire" accident, it does not mean the fear of such an event should keep us from taking on the likes of Hitler, etc.
Likewise, the fear that a jury might accidentally send an innocent man to execution should keep us from defending the lives of our citizens by demanding the highest price be paid by the convicted perpetrators. That fear should be virtually nonexistent now, thanks to DNA testing. And I can't think of many cases these days that would result in this punishment that would not have some sort of DNA evidence either damning or acquitting the accused.
IOW, risk analysis strongly points to continuing on with executions post-haste, when the crime warrants it. And far worse things can happen to a man than the apparent premature end to their life.