Frank James is taught the hymn, "The Old Rugged Cross", but this was not written until 1912. While Frank lived until 1915, Jesse was killed in 1882, and Jesse is still alive when Frank learns the hymn.
When Frank is in Colorado across from and watching Ford's bar, a drunk is thrown out of the bar. Frank stands up with no hat on. After the camera angle changed, he is wearing a hat, and then on the next camera change his hat is off.
The opening minutes are set in early April 1882 in Missouri. As Jesse James walks to his house, the street and yards are covered in dead leaves and nearby tree branches are mostly, but not quite completely, bare. The scene was likely filmed in the autumn months (of 1985).
Most of the Colt Single Action Army revolvers in the movie have bright brass trigger guards and grip frames. On real SAAs, these parts were made of steel or iron, then finished in a deep blue that matched the barrel and cylinder.