The "death penalty" costs very little - even with employee overtime and travel for execution team members, it wouldn't cost as much as a month in prison. This is a myth generated by anti-execution activists.The cost is in anti-death penalty litigation and that is because the government is paying both sides of the tab AND, more importantly, allowing government funds and appointed attorneys for purposes that are not constitutionally required. An inmate sentenced to death is entitled to no more appeals than any other, but for some reason we voluntarily allow government funded attorneys to spend millions of dollars on a standardized list of delaying actions that often go on for 20+ years - apparently every inmate on our death row has (a) been represented by the most incompetent attorney in history (b) just discovered he was mentally retarded and/or mentally ill at the time of the crime (c) just realized that some evidence disposed of in 1980 might have had DNA on it, etc., etc.
Frequently convict the wrong guy? Got a statistic on what you'd call frequent? here, even the few inmates we've released aftert the "innocnece project" took up their case have included some that were "probably" not guilty (far from clearly innocent) and at least one who definitely did it, but his lengthy, post conviction, hand-written confession was not admissible.