John D. Lee execution

The execution of John D. Lee was accurate for the most part with only a small error spotted. When you see the soldiers that execute Lee they have the wrong hat device on. They are wearing the correct uniform for 1877 with the exception of that. They are wearing the insignia of infantryman, the french hunting horn, of the 1860's. They were wearing the device that was worn on top of the forage caps. That insignia was then reduced in size so that it could be worn on the front of the kepi. But that same year, 1872, they changed the insignia from the french hunting horn to the crossed rifles. So in the movie the Army should have had the crossed riffles and not the French hunting horn. Did any body else catch that?