Schneider brings a piano into the Romano apartment so he can rehearse with Alex for a contest at the Lodge. At one point, Schneider sits down and plays some pretty spiffy jazz licks. His hands are in full view, and it is obvious that Pat Harrington Jr. is really playing what we're hearing (in the key of C major).
The title is a song written by Ray Henderson, Bud De Sylva, and Lew Brown features in The Singing Fool (1928) and sung by Al Jolson.