Visible crew/equipment: Near the beginning when the new recruits have arrived & are being harangued by the drill sergeant for the first time, in the shot where he walks along the line of recruits towards the camera you can see the camera dolly tracks on the grass. Then when the angle changes to a long shot you can see the marks left in the grass by the tracks.
Trivia: John Travolta was offered the part of Mayo first but turned it down to get his pilot's license. This is not the first part Travolta gave up and Richard Gere later got: he also gave up the lead in "American Gigolo" (1974). Also, Gere was originally supposed to play Danny in "Grease" (1978).