Pretty sure we used to use the bodies of executed murderers for medical research in the 17 - 1800's.
If the person involved says yes then there is no problem. What is a bit of a problem is the suspicion that some of those on death row are moved forward, sometimes with no last visits from family, to "accomodate" the transplant operation (Any one seen the film "The Island"?). I think there was mention of a few non-death row prisoners also, shall we say, being put in a position where they could donate their organs also.
Organs are now big business. Over in Brazil there are gangs scooping eyes out of people to sell for the corneas (I think). It is a situation that needs to be looked at. As it involves the greatest of motivators (life for the recipient, large amounts of cash for the provider) and the greatest of downsides to the "doner".
whats wrong with taking organs from executed people. If they're being executed in the first place, you have to assume they are guilty of a bad crime. In this case the only useful thing to do with them is to chop them up and sell them for a good purpose.