An unattractive feature of execution in the USA is that condemned men linger in prison for years awaiting execution. This is done, I suppose, to give them every possible chance of appeal; but it greatly prolongs their suffering.
If your country has a policy of execution, some innocent people are bound to be executed regardless of how long is spent in the appeals process. I think you just have to accept that, or give up the whole idea. Better, then, to abolish Death Row. Murderers should be tried with all possible care, but if found guilty they should be executed as quickly as possible, ideally within minutes of the sentence being pronounced.
I doubt that the saving of an occasional innocent from execution is worth all the suffering inflicted on those in Death Row -- including that inflicted on the innocent who is eventually saved. Better to kill a man quickly and be done with it than to keep him in prison for years with death hanging over him.