The "media circus" surrounding Gary Gilmore's execution was due to a few factors:
1) He was the first person executed in the United States after a 10-year moratorium
2) He never appealed his execution and, in fact, protested whenever it was appealed on his behalf
3) Perhaps most importantly, Rolling Stone sent his brother Mikal to cover the execution. It's a hell of a read. Google "my brother Gary Gilmore" and you'll find a .doc of the whole thing.
Something else to consider is that "humane execution" isn't exactly something the human race is just now grappling with. Most cultures settle on beheading which is messy as hell. All that blood spraying about tends to be seen as barbaric. Nonetheless, the guillotine is about as efficient and humane as we've gotten it. It involves a lot of apparatus, though, so firing squads pop up instead (unless there are religious reasons for the spilling of gallons of blood in the public square - lookin' at you, Saudi Arabia). Pretty soon, that, too looks barbaric.
One of the most gripping passages I've ever read is the first words of Bertil LIntner's Blood Brothers:
Something not mentioned until later is that Chinese prisoners executed by firing "squad" (ie, a dude with an AK-47) are instructed to open their mouths so that the bullet will pass cleanly through their brainstem without messing up their faces. That way, their families aren't traumatized as much by the corpse. Which sounds barbaric as hell to our ears because we like our executions in the abstract - give the bad man some sleepy sleepy drugs and it ceases to be a problem.
What we're seeing here is the abstract becoming concrete.
That's the way we deal with the death penalty debate in the United States: "Do you, citizen, abstractly believe that an abstract prisoner who committed an abstract capital crime against an abstract victim should be put to abstract death by an abstract entity in accordance with abstract standards of morality and justice?" Because as soon as it becomes concrete, it becomes about vengeance, not justice.
John Oliver had a great take on it last Sunday. He made the point that even if you know 100% the criminal is guilty, and you know 100% that the victim's family wants the criminal put to death, do you want to live in a country that gives them what they want?
Sorry. Complex issue for me.