Personally, I believe the death penalty is bad public policy, but not morally wrong, or a moral contradiction.

I believe it is bad public policy because yes, it is possible to be wrong and execute innocent people, and this has probably happened. Executions also create what sociologists have called the "brutalization effect." That is, murder rates actually go up following executions, so rather than being a deterrent, they actually seem to send the message that killing is okay. Executions are also incredibly expensive, from a more expensive trial all the way to the appeals and final act. Finally, executions are often doled out unfairly. For instance, in my state, Gary Ridgeway (the "Green River Killer") was able to bargain his way out of the death penalty, after killing nearly 50 women, because he got to trade on some information he had. Others, who have killed far fewer people, have been put to death, because they didn't have anything to make a deal with.

That having been said, if somehow public policy could be swept aside, and you had some sort of perfect realm, in which you could be 100% sure the person was guilty, I do not believe it would be wrong to kill them. To say that the executioner is just as bad as the killer, is to say that the killer and his victims are of equal worth. I don't believe that is true. I believe the killer voluntarily surrenders his social worth when he kills an innocent person. Take for instance Ted Bundy. To say that we're no better than Bundy for putting him to death is to say that Ted Bundy's life is equal to that of the 12-year-old little girl he ruthlessly slaughtered (not to mention the adults he killed). If you had to choose between Ted Bundy and the little girl, and could only save one of them, would you really flip a coin? No, you would save the girl. We instinctively understand that Bundy has less worth. I'm not saying you need to accept this as an argument for why executions are okay, but I think it does prove that executions are not a moral contradiction. An execution is not a murder.
Killers surrender certain rights when they take the lives of innocent people. I don't believe every murderer should be sentenced to death, but for many killers, they chose to kill because they enjoy killing. They selected an innocent person, murdered them for their own enjoyment, and walked away guilt-free. They do not have a moral high ground to stand on. When they whine and cry that they deserve life, what are they basing that on? The assumption that no one can ever lose their right to life, even if they deny that right to others? Where does that idea come from? Frankly, nowhere. I have never heard a persuasive philosophical argument to that effect, and most cultures have not accepted that idea throughout history. Ask just about anyone if they would kill Hitler in 1939, given the chance, and almost everyone would say yes.

I understand there is no perfect realm where you can be 100% sure. I guess my overall point is, I don't think it is a good idea for our society to put people to death, for practical purposes, but the people who threw the switch on Bundy (or Gacy, Fish, etc) can sleep easy knowing they didn't do anything morally wrong.