Anybody who is wrongfully executed was basically guaranteed to spend their entire life in prison. Death row inmates get dramatically more access to legal aid than anybody else rotting in a cell, so if they couldn't win their appeal, the guy doing life isn't, either.
Generally, I'm against incarceration for that reason. I think the relatively muted violence of it is too easy to stomach for the public, which leads to people letting the system get sloppy. For public and infamous crimes, however, where the question is not "what act took place", but rather "did this act constitute a crime, and if so, what is the punishment?"-type cases, I'm perfectly fine with capital punishment being on the table. We trust public officials with significant authority, and abuse of that authority is utterly irredeemable. Frankly, for elected officials I'd support a "two-thirds vote and you hang" policy. If you want power, and seek out power, you have an immense responsibility to live up to your constituent's expectations.