Wrong accusation is definitely a problem, but ultimately I think people should be free to decide what kind of laws they want. The Machinery of Freedom describes a government-less system in which people voluntarily pay an insurance which defines what the law is and what happens when the law is broken. If people have different insurance companies, they can agree what law is going to prevail in which cases. If capital punishment were something desirable (which I don't think it is: the risk of being wrongfully accused outweighs the potential deterrent to other to kill me) some agencies could evolve to cater to this need.

That said, I think there is an economic argument to be made against capital punishment.

Killing someone is definitely a waste of human life and economic potential.

Wouldn't it be better to have the sentenced man work for the rest of his life in prison and create value? You could potentially have a deal in which the prison organise the work, keep a portion of the profits to keep operating and pays the victim / victim's family for the crime they were subjected to.

I think this is fantasy right now because the government is terribly inefficient in everything they do - but with a system of private prisons (another fantasy, given the current trend of increasing the government size, instead of reducing it), maybe someone would be able to turn a profit and make it work.