Capital punishment Solution? or Problem?

My stance on capital punishment isn't so black and white. There's soooooo many factors that goes along with it. For instance what if you find out the prisoner was innocent after you killed him/her already? History is there to help us learn from our mistakes and capital punishment was a mistake, what makes you any better than the accused if you are killing them as well? There might be retribution for the family of the victim but how long will that last? It wouldn't solve any crimes or somehow prevent them from happening if criminals have no alternatives.I do think there are a few exceptions for the real serious crimes, one murder is bad enough as it is, but why not give them a second chance after reform? Isn't it a Christian principle to give second chances or that doesn't apply somehow?