In the movie you see that Gary Gilmore shot himself in the left hand, but in real life he shot the right hand.
When they are releasing the straps from Gilmore after he is dead you can see his hand move. In addition the arm is closer to the leg than depicted in the previous shot.
Gary Gilmore was described as having watery-blue, piercing blue eyes by numerous family members, and even a witness to the 2nd/Bushnell killing. Yet they missed the mark by casting brown eyed Tommy Lee Jones in the starring role.