The idea of Lucy and Ethel telling the boys that they cleaned their old dirty clothes with gasoline, only to have them go up in flames when they got near the stove, is in actually an old fashion way of cleaning them. Prior to the advent to the automobile gasoline, a byproduct of kerosene, only practical purpose was in cleaning clothes. With the advent of the automobile in the 1900s, it was seen to be the perfect energy source to power the combustible engine. Automobile use and the knowledge of gasoline's highly flammable nature lead to the development of much safer laundry detergents. Using gasoline to clean clothes fell out of favor in the 1920s so even for 1953 Lucy and Ethel method for cleaning clothes would of been seen as quite archaic.
Lucy, Ricky, Fred, and Ethel go to the movies to see a Marilyn Monroe picture. The movie title isn't mentioned. However, this episode was broadcast in December 1953. Marilyn's big hit Gentlemen Prefer Blondes (1953) was released in the U.S.A. in July 1953, so most likely the movie the four went to see was How to Marry a Millionaire (1953), which was released in the U.S.A in November 1953.
The man doing the brief trumpet solo is Tony Terran, who was with Desi Arnaz's orchestra for many years. Terran did a lot of studio and session work in the 1960's for various TV shows and recording artists.