While Fred and Ginger are seated watching the Carioca, their position changes; first she is on his right, then she is on his left, and before they get up to dance, she is back on his right.
Although it's supposed to be in flight, one of the planes in the big wing-walker sequence has a bad matte effect at the bottom of its wheels and visible tie down wires attached to its tail. The same mistake can be seen on the plane in at least three shots.
Just after the flying sequence with the wing dancers there is a scene with characters sat on the terrace. The back projected image is to the wrong scale resulting in someone with an enormous head being next to the parapet.
From the height they were flying, most of the "dance" routines of the young women on the plane wings would not be visible to people on the ground.
The Haitian at the golf club has a British accent, but Haiti was never British. He should have a Haitian accent.
The violinist in the section where Fred is working with a group of inexperienced girl dancers has his bow set between the strings and the back of his violin. At the end of the number, the bow is used correctly.