When Jim is coming in to land after stunting over the Havana airport, we get a good look at the writing and symbols on the right-hand side of his plane. When he actually touches down, they are in different colors and positions, and a diagonal line of bullet holes has appeared.
When the search plane first spots the wreckage, the mirror signal flash comes from off the right wing of the plane wreckage and across a stream. Seconds later as the pilot looks again, the mirror flash comes from directly in front of the nose of the plane wreckage. Since the crashed pilot was hurt and had to drag himself to the mirror, he couldn't have traveled that far in such a short time.
When Jim and company are trying to land through the fog in Cuba, from inside the plane the propeller is seen to stop, but in the next long shot (of the model) the prop is still turning, then comes to a stop.
When the camera moves from a position between Sally Eilers' and Richard Barthelmess' hotel rooms to the left, her room can be seen from his, revealing the missing fourth wall of the set.
When Neil and Jill are inside the passenger plane talking to the friend who had seen Neil's brother Jim, the view out the window beside Jill shows the plane at first parked (as the pilot excuses himself and moves up the aisle between them to take the controls), then begins moving on the ground and picking up speed and taking off. But the entire time, the sound of an idling engine is heard very loudly in the background. The engine sound should have changed to a high-rev sound for takeoff.
When the parachute is pulled from the tree, you can see the ropes that had been holding it there in place to support the weight of the parachutist.
Neil's plane goes down en route from Havana to Mexico City and the radio announcer gives his estimated position as 22°N 88°W. This would be off the Yucatán Peninsula about 400 miles west of Havana, which makes sense. But when Jim and Jill get to the airport, the position marked on the map is south of the Dry Tortugas. This would be about 24°30'N 83°W or about 100 miles north of Havana, and Jim's compass shows him flying north to reach the site.
The Amarillo and Havana airports show significant mountain ranges in the background. However, both airports are situated in areas that are geographically very flat with no mountains to be seen for hundreds of miles.