When Cooper walks out of the house he's holding a .45 Automatic pistol on Ginny. During the next few minutes the position of the hammer on the gun changes from down to up and then down again.
When the forest ranger looks at the plane, clouds are reflected in the binocular lenses, but when the shot changes to the plane flying, there are no clouds visible in the sky.
The plane spotted by the ranger had a low wing configuration- the wing was below the cockpit. The plane spotted by Mathews on the ground had a high wing configuration, so 2 different planes were used for this footage.
When Mathews and the Patrolman find the plane. The Ranger's jeep is so close to the aircraft, Mathews would have noticed it and the body of the Ranger. Instead he walks off to search for the occupants of the plane.