When Gilda is brought back to Argentina by Tom, she slaps Johnny hard across both sides of his face. In reality, Rita Hayworth's smacks broke two of Glenn Ford's teeth. He held his place until the take was finished.
In the V-E Day scene, the crowd in the Casino is singing the 'Marcha de San Lorenzo' (San Lorenzo's March), instead of the Argentine national anthem (which would have been the logical theme to sing at that occasion). This piece of music honors a famous battle in Argentine history, and is usually played only in the festivities related to Argentine hero José de San Martín.
There is a rumour that this film is the only time you hear Rita Hayworth's real singing voice but it is sadly not true. According to the bonus features from the DVD, Rita actually never recorded her own singing voice and was a talented lip-syncher. Anita Ellis dubbed almost all of her singing in Gilda. Rita always wanted to do her own singing, and Columbia Pictures chief Harry Cohn paid for her voice lessons, but she never developed a voice he considered strong enough to be used, and Rita remained bitter about that for the rest of her life.