On capital punishment... the trouble is what to replace it with. Prisons are also barbaric and uncivilized and a waste of life. Plus they cost more. Plus there is the tendency in the US to privatize them, which leads to perverse financial incentives to put more people in prison. So we have the highest incarceration rate in the world.
Yet no-one has figured out how to get rehab right. And if rehab were successful, it would be too much an invasion of a person's privacy; it must be, in order to be successful: to change the person's way of thinking (which led to the undesirable behavior), permanently. If it were successful then the application might be broadened, until a pretty large fraction of the population is in some kind of rehab/reprogramming, even more than to the extent that we have too many in prison now. As now, society could just continue to say that when you commit a felony you lose your rights, sorry about that. Then continue lowering the bar, until there are a lot more felons available for the service of the state (or the privatized institution).
So whatcha gonna do? I think first of all we should quit putting people in prison for not-so-serious reasons (number one being drug offenses) and find quicker, more effective punishments for all the fraud/theft type stuff (e.g. some sort of multiplicative restitution when possible, or a better education and a chance to start over in cases where that might work better). What good does it do for taxpayers to pay Madoff's room and board for life, even as badly as he screwed up? He still has a useful brain, and after being so thoroughly discredited as a financial guy, maybe could go on to do something completely different, if we let him. He could be put back in square one with only the most basic possessions, and allowed to start over in a different field.
In cases where murder 1 is 100% certain (which as you point out, is never) I don't in theory have a problem with capital punishment. It's no worse than the murder, and there are people with such twisted ways of thinking that they cannot live normal lives without doing things like that. But yeah, there are all the incorrect convictions to worry about. But I'm not sure that life in prison is better. Maybe if prison were more like a constrained but semi-normal life, were there aren't opportunities for further murder, and no opportunities to get raped by the other prisoners, but there are opportunities to do something good. I don't care about the perception of "justice" from outside as much as whether we have a solution which works in the best way, what to do with this human capital which has gone awry. We haven't been going towards that kind of goal at all. I think all the efforts we have made are bad enough, that you can't just say capital punishment is the one thing which is so barbaric that it ought to be banned.