Ever long chain of death?

So The Green Mile is up there in my favorite movies, and it makes me think a bit.  Some states allow the death penalty, while some find it cruel and inhumane.  
        In the movie the jailors execute the lives of murders and other criminals; and this is where I start to think...
  What gives the jailors the superiority to kill the murders without them being punished themselves? 
Yes, a job is a job, but that doesn't give them the rights to kill without persecution...  and I'm all for the death penalty (eye for an eye, tooth for a tooth)..  But wouldn't this just create a big chain reaction of killing?  Though the jailors who executed the criminals had a legitimate reason to do so and was chosen to do so through a court of law, isn't it still wrong?
         Though it is part of the jailors to execute the criminals, does it morally condemn them because they are also doing an act of murder?