...The death sentence is barbaric and solves nothing. And obviously doesn't deter crime....
Regardless of whether someone is innocent (which, I agree, has happened and will continue to happen), we must first analyze something like a death penalty. First, let's define the thing: what is a death penalty? Is it electrocution, hanging, lethal injection, beheading, stoning or what? Is it slow, quick, painful, painless, private, public? Each of these have been done, plus many others. Is one 'better' than another? Let's keep this thread in mind as we move on to what a death penalty is supposed to achieve.
Ideally, a death penalty is the ultimate token of punishment for an act of sufficient criminality. In this case, it serves not only to punish offenders but - hopefully - deter future offenders. The argument should be that the 'cost' (i.e. death) significantly outweighs the 'reward.' Now there are also implications that the mechanism is one of 'revenge' for the victim). So let's consider what we've got: a mechanism of death that seeks simultaneously to punish, deter and satisfy (i.e. victim satisfaction). If you're going to use something like the death penalty, how do you best achieve all 3?
Examining the West, particularly America, lethal injection in a highly controlled environment seems to be the preferred modern method. It is touted as the most humane and leads to the least suffering. An audience is allowed to view the injection, but as the inmate loses consciousness curtains are drawn and the viewing room is emptied. Certainly dying is a terrifying prospect, but as far as deaths go this is not the worst one could imagine. In fact, if your only option is to die a grizzly death at the hands of a fellow criminal or take a chance and potentially face this type of death penalty...well, the choice becomes obvious. As well, the victim, while allowed to view the injection, sees no suffering or the final moment of death. I argue that this, therefore, only achieves the goal of punishment and, even then, does so lightly.
What does that mean? Well, I think it means this: if you're even going to do something like the death penalty then you need to do it right. If you are going to entertain such extreme notions it had better be to achieve EVERY goal you set out to achieve. Therefore, it only makes sense to have the death penalty be absolutely brutal and terrifying. It should be barbaric, humiliating, massively public and awful for the inmate. I say again: if you will kill people to achieve your ends, then do not make half-measures.
So - we now have a terrifyingly brutal system of ultimate penalty. HERE is where the false positives come into play: not everyone has been correctly convicted. Under the current system, which is awful yet 'light,' perhaps some pundits can overlook the false positive rate (since, presumably, it's so low). NOW, however, since things are as brutal as possible, even a single false positive will call into serious doubt the punishment. You have two options: you can only punish perpetrators that are CLEARLY guilty of some unforgivable crime, or you have to abolish your death sentence.
Option 1: If there is any doubt, the case would not move to the death penalty. Now, again, the reward vs. risk ratio is balanced toward risk. This is because VERY few cases have evidence that is so cut and dry. The number of absolutely provable cases warranting execution would be small enough that it would no longer achieve the goal of deterrence. We're right back to square one, only now the system is not only ineffective, it's also terribly barbaric.
Following all of this logic, if you are still concerned with being moral (which, btw, a justice system like that of the United States is indicative of (if you were immoral you'd have no justice system (what would be the point?))), then the ONLY reasonable option is 2: total abolishment of the death penalty.
In conclusion, if any justice system considers itself to be, or seeks to be, moral, then the death penalty can never serve as a useful countermeasure against certain types of crime, or to provide closure to victims. It is simply an immoral act on all accounts.