Revealing mistake: In this scene we see Frank Sinatra in a diving suit and helmet being lowered into the sea to look for a sunken submarine. As he is being lowered you can see the sun's reflection on the walls of a tank, meaning it was filmed in a large tank of water.
Visible crew/equipment: When the submarine is below the Queen Mary and the ship starts moving forward you can see a human hand holding the stern of the submarine as it is tossed around by the propellers.