The film is set in 1864 but the pistol a trooper uses to nail up a picture appears to be a Remington model 1875 Single Action Army Revolver using metallic cartridges which wasn't introduced until 1875. He should have carried either a Colt 1860 Cap & Ball revolver or a Remington 1858 Cap & Ball revolver.
While set during the Civil War - the carbines the Cavalry uses in the film are model 1873 or later Springfield "Trapdoor" models. You can see people in many battle scenes flipping open the actions to reload.