Continuity mistake: When Remo Gaggi is talking to Andy Stone about Ace cussing out the Board, there's a pack of cigarettes beside Gaggi in his car. The camera angle changes to show Stone's face, who is outside the car, and when it flips back to Gaggi, there is a Zippo lighter in place of the cigarettes. The camera goes back to Stone, and when it comes back again, the Zippo is gone and the cigarettes are back. And to top it all off, not once did Remo smoke in this scene.
Continuity mistake: When they are in orbit and Fred vomits you see Jim taking off his suit and an open hatch to the LEM which has not been docked yet. Later when preparing to jettison the LEM you see Jim closing the hatch over this tunnel.
Continuity mistake: Early in the movie when Thomas falls overboard, John Smith ties a rope around his waist (00:02:56) and jumps in after him. Thomas is very far away from the ship (00:03:12). But when the men pull John and Thomas up, John is holding on to the rope with one hand and the end is left dangling (00:03:36). One of the men who pulled them up then coils the rope with a mere two coils (00:03:48), not nearly long enough to have reached Thomas while he was overboard. In the same scene, when we are viewing the men pulling John and Thomas up from above (00:03:38) there is no extra rope at their feet as there should have been for such a long rope.
Continuity mistake: In Morocco, when Lee, Capby, and Roberts take off, they still have their external fuel tanks under their wings, indicating they have not entered combat. As they are flying and do their mission, they have dropped their tanks. But after Lee says "let's head for home," you see one Mustang landing, external tanks and all.