After the plane General Dennis tried to talk in to a landing crashes, the next scene is an inside shot with the generals discussing allowing staff photographers into a debrief. On the brick wall in the background, the shadow of a boom mic is clearly seen moving in and out of scene for the entire duration.
When Van Johnson is in Gable's office alone in the very beginning of the film, someone comes in and gives him a model plane and he places it on a shelf behind him. However, when Gable comes in soon afterwards the shelf is empty.
The goof item below may give away important plot points.
When General Dennis unsuccessfully tries to talk down a crippled bomber, he is shown with a microphone in one hand. After the bomber crashes, shots of him leaning on a rail with both hands are interspersed with shots of him with one hand still on the microphone.