I think there are a lot of misconceptions regarding the functionality of the knot. In England from about the mid-19th century on they used a simple slip knot, and that broke the neck just as nicely as the larger, more elaborate version. I keep hearing about the knot having the purpose of striking a blow against the victim's head, but I'm not too sure just how that works. In this case it looks like it at least left an abrasion. Old Saddam probably never knew what hit him.
The last US hanging by federal authorities was in 1959. It was done at the Iowa State Penitentiary in Fort Madison, IA.