Toward the end of the film, when Terry is on the sofa talking to Michel, she offers a cigarette to him. He picks it up, puts it in the mouth a little while and takes it out. Next shot, the cigarette is in his mouth.
When Michel is waiting for Terry on the Empire State Building into the evening, and a thunder storm breaks out, the same forked lightning strike is seen at least 4 times in the background, always in the identical location - which is highly unlikely.
When Irene Dunne and Charles Boyer are on the ship during the day and they are next to the railing talking and reading their letters, the ocean is moving behind them. Just after the close up on Dunne, she turns and faces the ocean, but you can see the shadow of her head on the screen that displays the ocean.