Does the state have the right to execute one of its citizens?
Sure—there are individuals who are beyond the pale. Society has a right to expunge such members from its ranks—permanently and irrevocably, if their actions warrant it.
Leaving aside for a moment the question of where to draw the line between members of society who deserve to be rehabilitated and members of society whose actions are unforgivable, there is no question that such unforgivable members exist, and should be executed. Jeffrey Dahmer is the perfect example: A pederast, a murderer, and a possible cannibal. Need I say more?
The problem isn’t whether there are such human beings whose actions merit their execution. The problem is the mechanism a society uses to determine guilt or innocence.
All human institutions and mechanisms are fallible, by definition. To claim that any justice system never errs is ridiculous. There are cases such as Dahmer’s, where there is no doubt as to guilt or innocence—but those cases are exceedingly rare. Most cases are sloppy, with no clear-cut evidence, no smoking gun, no video-tape to prove without question that the accused is guilty.
Aside from the fallibility of the justice system, there are the individuals who operate that justice system—their motivations and actions. Mark Furhman, he of OJ infamy, wrote an extremely interesting book called Death and Justice, describing how he became convinced that an Oklahoma prosecutor and a forensic lab technician were, in essence, manufacturing death-penalty convictions. In 2001, out of the 21 people executed in Oklahoma, 13 were convicted by this pair. It’s a horrifying story, backed by solid reporting, of two criminals manipulating the criminal justice system, and the damage they wreaked. I have no doubt it’s not the only instance.
A falsely convicted man can be released after years in prison. But we've yet to figure out how to raise the dead.
So in principle, yes, the death penalty is acceptable. But in practice, no, it is not.