Regardless of the financial aspects of death penalty cases and the appeals process, there is no doubt that execution is a deterent to continued criminal acts, and it is a deterent to some people, preventing criminal acts.
The error of false conviction resulting in death sentences would be lessened if the rules of evidence were more stringent, and if false evidence and testimony (on the part of any party - prosecution or defense team or witnesses) was punished by the same penalty ascribed to the quilty and convicted perpetrator.
The problem we need to address is the use of circumstantial evidence to obtain convictions, instead of multiple eye witnesses being required to convict in a death penalty case. I do not support the death penalty if there are no eye witnesses. I do support the death penalty when multiple eye witnesses testify to the quilt of the accused, and I believe that execution should occur within a very short time of the sentence being passed by the court. I believe execution is appropriate for crimes of murder, rape, and sexual assault of defenseless children and the aged.
The business of automatic and multiple appeals being required before execution is performed, is due to the lack of confidence in the justicial system, and fear that we are actually convicting an innocent person. Remove the lack of confidence in our judicial system, and get rid of the costly and time consuming appeal process; then the cost drops to the point where it is cheaper to execute than to support prisoners for life.
The concept of cruel and unusual punishment is sometimes raised by those opposed to the death penalty (and is also used to require coddling prisoners by giving them entertainment, exercise equipment, etc). We need to determine what constitutes institutional cruelty (torture, maiming, starvation, deprivation of medical care, etc) and realize that what is unusal now was once the norm in the area of punishment.
In the early days of this land, people were placed in stocks in the public square, so that they would be humiliated, and the shame would give them incentive to do the right thing. That is now considered unusual, and not to be allowed. Our judicial system now says humiliation is worse than incareration at public expense; we can put people in jail for years, but we can not publicly humiliate them for a week or two. It would be far less expensive to use the humiliation type punishment for first offenders (minor crimes) than to give them painless warnings and then incarcerate them later as more hardened offenders for long periods of time.
The death penalty has an appropriate place in our judicial system; we just need to be wise in its application, and quit abbrogating our duty to determine its proper application.