The song that Graff repeatedly whistles, and is sung by the men accompanying him, is Unreconstructed Rebel aka Good Ol' Rebel. The song was not written until 1914, many years after the setting of the movie.
As the outlaws head "east" (after much discussion and emphasis that they are going east instead of south) their shadows appear on their right as they ride, indicating that the sun must be shining from the north.
At the beginning or the movie, we see a screen banner telling us the story's setting is New Mexico and takes place in 1873. Many of the characters use a Colt Single Action Army Revolver, some of which show significant wear. This pistol was introduced in 1873. It is unlikely that such a large number of the characters in this movie would possess a weapon that had just been released, especially with noticeable wear and customization (nickel plating, pearl handle plates, etc.).