Both the Bible and the US Constitution clearly allow for capital punishment. Saying that either does not, as some do, is simply not true. As for documented mistakes, I'm pretty sure you have to go back quite some time to find them.
The foundation of American law in a Constitutional democracy is that it is better that 10 guilty people go free than one innocent person serves in prison. This is why there exists the assumption of innocence until guilt is proven. What is a good time line for the innocent to die or even evidence that would suggest doubt towards guilt? Twenty years? Thirty...forty...or how about just seven years ago?