The problem is not with the death penalty in the abstract. As others have pointed out, the modern state is the vessel into which we place the power of War and the power to take away rights from criminals.
The problem is that far too many police and judges are corrupt and and incompetent. It just doesn't work well in practice.
Contrast the death penalty with war: As Rumsfeld said, "Stuff happens." When you are not in a war zone, you expect to get justice at a pretty high quality level. In the U.S., education has been dumbed down to the point where graduates of the 2 year law enforcement programs at community colleges have on clue what the Constitution means. They are the willing armed force of the bureaucracy.