The music was played by pianist Carmen Cavallaro in his own style. He had a completely different, and more technically precise, style of playing than Eddy Duchin had. The orchestral arrangements and style of playing are also anachronistic - Cavallaro's of the 1950s versus Duchin's, typical of the late 1920s and early 1930s. (Duchin's orchestra also included a tuba and banjo). If you listen to recordings by both, this is clearly evident.
The Central Park Casino was portrayed in the movie by the famed Tavern on the Green, also located in Central Park, since by the time of filming in the mid-50s the casino was long gone.
From 1946 onward, after Eddy returns from World War II, all of the women's hair styles and clothing, particularly those of Victoria Shaw, are strictly 1956, often quite distant and different from those worn by women in the period being depicted. And in just about every scene in which automobiles are involved, contemporary mid-1950s models can be seen all too prominently in the background.
From several shots, including continuous shots from hands to face, it is evident that Tyrone Power mimed the piano playing himself, no mean feat.