However, despite all of the potential for error that exists, I cannot think of a single example of a person who was executed in the United States who did not commit the murder or treason that s/he was accused of.

Please allow me to introduce you to Larry Griffin, well on his way to becoming the first confirmed wrongful execution in the history of the United States.  (This is not to say that there has never been another; but this time, pretty much everyone agrees.)  While Mr. Griffin's life history proves that he was definitely a bad apple, he was not sentenced to die or actually executed for being a bad apple, something which still presently does not violate any known law all by itself, let alone support the special circumstances all by itself to support a lawful capital sentence.  Mr. Griffin was, instead, executed for a murder that it now appears increasingly certain (to everyone but the prosecutor who will end up with Mr. Griffin's blood on his hands and conscience), that Larry Griffin did not in fact commit.  Of course, the "investigation is still ongoing" but frankly, there's not much left to investigate since both Mr. Griffin and the primary eyewitness used to convict him are both dead; except of course, an investigation into how the State of Missouri can actually insulate itself from both the legal liability and the utter undermining of its capital punishment system if it admits that, yes, it executed an innocent man.  

However, if the Streamlined Procedures Act of 2005 continues towards passage at the rate it is racing through both the House and Senate, Mr. Griffin will eventually become just another another statistic of the "mistakes" of the (in)justice system where capital punishment is concerned.  Given how little hell has been raised by progressives over the Griffin case, it seems that this type of collective "shrug" in response to the possibility of wrongful execution is where the country is heading.