I think with advancements in scientific evidence to support traditional evidence like CCTV, witness testimonies etc etc its very likely the conviction would be "safe" and generally the people who are getting found guilty of the most heinous crimes, the ones that the death penalty would most likely to apply to, are guilty as charged.
But there is always a risk of a miscarriage of justice and that's where this argument falls apart for me.
Also, if you look at the USA a lot of death row prisoners spend years and years waiting to meet their maker and I don't agree with that either.
If you're going to put somebody to death do it there and then, don't keep them waiting every day thinking each day may be there last for years on end. However, the way our justice system is set up, with the ability to appeal and have retrials etc, killing somebody immediately after a guilty verdict just isn't possible.
Then there is the method of killing, this country cant even decide on a way to kill livestock with 100% support so don't fancy the chances of one being agreed on for humans.