When Ricky drops off Lucy at the studios, he says he's meeting with "Mister Minnelli" as in Vincente Minnelli. Vicente Minnelli directed Lucille Ball and Desi Arnaz the year before in "The Long, Long Trailer."
The movie that Fred and Ethel make is never mentioned again after this episode.
Lucy goes to sit at the soda fountain at Schwab's Drug Store in Hollywood with hope of being discovered. Schwab's was a legendary drug store and soda fountain that is best known for the Hollywood myth of actress Lana Turner being discovered their by movie producers while drinking a soda (Bobby the bellboy relates this story to Lucy which is what inspires her to go their). Schwab's remained a Hollywood landmark until it closed in 1984.
Ethel had announced in Albuquerque, in "Ethel's Home Town" (#4.15), that she would star in a film in Hollywood. She and Fred land character roles in a movie, which will give them two weeks of work at the studio. This development gives truth to her previous lie.
When Ricky comes back in the hotel suite from reading Lucy's postcards he refers to Carolyn Appleby as Lillian Appleby. That was her original name during her first appearance but they switched it to Carolyn for the remainder of the series