I do not support the death penalty in the United States for one basic reason: there is no way to ensure that mistakes are not made. I do not trust the state (any state) to get this most important decision right. There are plenty of examples of innocent people being released from death row.
Has anyone ever been falsely accused of doing something they did not do? I sure have. When I was a child, I was in the wrong place at the wrong time twice, and was accused by the police of doing something that both times I had absolutely nothing to do with. Both were property offenses that other kids had committed before I wandered into the area. Those experiences have stuck with me as real world examples of the reality that those who are accused are not always guilty of what they are accused of doing.