The scene where Binghamton catches the crew in their costumes, the snow on the captain's hat disappears and reappears over and over.
When Tinker is pushed out of the plane, his parachute pack gets caught on the bottom of the door opening. One second later, the pack moves away.
When the Japanese officer says that "all you lucky Yankee going to stockade", you can see on the ground in front of McHale and the officer, the shadow of a camera man. The shadow becomes larger and clearer on the men's clothing as they walk out of camera shot.