When Ewing is shot and falls off of his horse, his foot slips THROUGH the stirrup. When the horse gallops away, the foot of the stuntman doubling for Jason Robards is TIED to the stirrup by a long strap that can be safely released.
After Ewing is told he will lose his ranch if he doesn't allow testing for oil, Frank and Ella are shown chasing cattle while swinging their ropes...left handed. In the next scene, they are shown roping right handed.
When there is oil miners explosions in the valley, sound of the explosions is heard at the same time as they are seen. Distance to explosions is 1-2 kilometers. In real life sound would come 3-6 seconds late..