Parker Brothers commemorated this episode when they made one of the six tokens in their "I Love Lucy" Monopoly a loving cup.
Like "Deep Sea Fishing" (S6;E7) and "The Golf Game" (S3;E30), this is another episode whose plot was most certainly created because of Desi Arnaz's love of sports. He loved horse racing and owned several racing horses throughout his life. When he retired he bought Corona Breeding Farm and bred his own race horses for several years.
Lucille Ball had claustrophobia so the prop designers had small eye holes carved into the decorative design on the cup so she could (somewhat) safely move around the stage.
Lucy and Ethel take the Lexington Ave subway in this episode. Note the great care Lucy set designers go to make sure the subway has the correct destinations posted. Traveling downtown Lexington Ave trains start at Woodlawn in the Bronx, then travel down Lexington Ave on the Eastside of Manhattan, and eventually terminate at Flatbush Ave in Brooklyn.
This is the last time that the Club Babalu (formerly the Tropicana) set is used during the series. The angle of the banquet tables (plus the fact the club was remodeled in "Lucy and Bob Hope" (S6;E1), make the room almost unrecognizable.