According to the lettering on the front window, the NYPD precinct Lucy and Ethel are taken to is Precinct 31. NYPD has no Precinct 31, but Precincts 30 and 32 are in the Manhattan North NYPD Borough, and according to the address provided in earlier episodes, the Mertz apartment house is also in the Manhattan North Borough.
The Ricardos' telephone number is revealed to be Murray Hill 5-9975. This will change during the course of the series, as various real telephone numbers go in and out of service. New York Telephone would advise the show's producers which numbers to use. In the mid-1960s, to avoid using actual telephone numbers, movies and television shows adopted the KLondike 5 number, which translates to 555 when all-numeric dialing started in the 1970s.
The real last names of the policemen are used. Officer Jenkins and Officer Nelson are Allen Jenkins and Frank Nelson.
At the beginning of the episode as Ricky reads the issue of TV Guide, you can see Queen Elizabeth II on the cover. This was the May 29, 1953 dated issue which was corresponding with her coronation ceremony that was televised worldwide on June 2, 1953. This was the issue out when they filmed the episode on May 22, 1953, and it would have been recognized and seen as timely when it aired on June 22, 1953.
Allen Jenkins reprises his role as a policeman in the Ricardo and Mertzes' neighborhood. Here, he works at the 31st Precinct.