When Indy arrives in New York, the sign on the building says "Grand Central Station". The actual name is "Grand Central Terminal", "terminal" being standard railroad nomenclature for the end of a line. There was a "Grand Central Station", but only until 1910.
Key Pennington's song "Come On and Kiss Me" is depicted in the middle of Act 1 of George White's Scandals of 1920, but historically, it opened Act 2.
When the Irving Berlin character plays "A Pretty Girl Is Like A Melody" on the piano at the Horseshoe Lounge, he fingers mostly white keys. In actuality, Irving Berlin famously could play only in the key of F-sharp, which is mostly black keys.