Dr. Protess' journalism class at Northwestern, has delivered 10 people from death since 1991. These students re-examined the facts, sometimes using new DNA techniques, sometimes using legwork, and were able to prove their innocence.
The students most recent release came about when they interviewed the eye witness used to convict a guy named Porter. The eye witness confessed he hadn't seen anything, but only went along because of police pressure. The police didn't bother to investigate, using only the testimony of their eye witness.
The local DA pointed out that this showed the system works.
These 80 released death-row inmate represents a lower bound on the fraction of innocent people awaiting execution. How many more would be discovered if all the cases were independently examined?
The cost of execution is the price of innocent people killed. I don't know how to calculate that number but it doesn't seem that retribution and vengance balance it out.