According to Desi Arnaz's autobiography, he and Betty Grable had dated when they were both in neighboring Broadway shows, not long before Desi met Lucy.
Before the number "The Bayamo" begins, a man named Jack tells everyone to take it from the top. After the number, Ricky addresses Jack saying, "How was that for you, Jack?" Most likely the actor playing "Jack" is Jack Baker, the person who was the dance choreographer. He isn't listed in the acting credits, but only as the choreographer, even though he has dialogue in the scene.
The Ricardo's horse,Whirling Jet, race was held at the Roosevelt Raceway. The racetrack was located in the Westbury section of Nassau County Long Island and held trotting races from 1940 to 1988. After its closing it fell into disrepair and was eventually demolished in 2001.