I agree with you, but I can think of another reason to petition against the death penalty besides mistakes. I don't think we should grant that kind of power to states because they tend to misuse it. This is more apparent in less democratic states, where the death penalty is an easy means to silence opposition.
With that said, the US is surprisingly slow in abolishing this horrendous practice, especially if you consider this graph in this link: http://en.wikipedia.org/wiki/Use_of_capital_punishment_by_co...