When Joe's plane clips the tree and loses the right wing, the plane rolls to the left. In fact, asymmetric lift would roll the aircraft to the right due to greater remaining airfoil surface on the left side.
When Carter is shot by Jean Arthur's character, the hammer on the the revolver had not been drawn back. A revolver will not discharge from just being dropped on table unless it had been cocked; and even then it's not a certainty.
Toward the beginning of the movie, when Tex the lookout radio guy says, "OK, it's open," you can see the whole mountain range in the background slightly shift to the right. (Apparently, somebody was moving the set backdrop or bumped into it while the scene was being filmed.)
When McPherson takes off with the patient, the chimney smoke shows he's taking off with the wind instead of against the wind. Taking off against the wind would increase his relative speed and help him take off.