There seem to be two reasons why people are against the death penalty:
1) Objection to the taking of a life (even if he is guilty) on moral grounds.
2) Objection to the death penalty because of the possibility that an innocent life is taken in error.
My thoughts on (1):
If the guy is guilty (and for the sake of my argument in point (1) I am going to stipulate that he is guilty), I don't have a problem with the death penalty for the following crimes:
Murder (1st degree, planned)
Rape
Child molestation
There are no mitigating circumstances for these crimes, and any individual who commits one of those three crimes forfeits his right to his place in society immediately. He knows the risk before he does it. You don't put down all your chips on one number at the roulette wheel and then cry when you lose. You don't reach out for those chips afterwards. They are gone. If you were concerned about losing them, you should not have bet them in the first place.
My thoughts on (2):
This is entirely a matter of evidence. It comes down to whether the evidence against the accused is relevant and is of the required quality. And I agree that mistakes do happen, whether they happen at the time that evidence is collected, or the time that evidence is analysed, or the time that the analysis of the evidence is presented. The evidence has to be unshakeable. This is a real concern. At the moment one form of evidence that I think is unshakeable is DNA evidence. And even so, to protect against mistakes related to evidence handling (or even nefarious laboratory activity) I would say independent DNA testing (by the defense team) would be required if there was to be confidence in the analysis. Ironically it is DNA evidence that has CLEARED many of the people who have been wrongfully executed. I suppose as regards (2) I would be more concerned about the kind of evidence that is being used to convict the accused. If the guy is caught in the act, arrested and confesses, I think that is good enough evidence to convict him. But I acknowledge that there are many cases where I would not be happy to see someone convicted, based on the quality and type of evidence being presented.