When MacGyver is climbing the mountain in search of the eagle, the length of his pants legs varies between shots, from knee-length down to ankle-length.
And when he's on his way down the mountain the the color of his clothes keeps changing, going from a blue shirt with a red cap to a white shirt with a yellow cap.
Because of the use of so much stock photography, Mac's flight went from semi-arid rock country, to dry grassland, to snow capped mountains.
It would impossible to shoot an eagle with a crossbow from a helicopter, as the downdraft from the spinning rotor would dramatically affect the bolt's flight.