At the beginning of the movie Viper is wearing the Lieutenant Commander rank. At the end, he is wearing the Captain rank. (The crew noticed this error the day after the scene was filmed, but Greg English was already on a plane from London to the United States.)
Due to the limited number of supporting artists allowed at some of the locations, some of them playing multiple roles. Most notably is the final scene. Maverick and Iceman's crew have the exact same people.