The British-accented character Eppy Brianstone is a parody of The Beatles' manager Brian Epstein. This is reinforced when the Brianstone character says that Pebbles and Bamm-Bamm will be the biggest thing since his group "The Termites" - another reference to The Beatles.
The title refers to Irving Berlin's anthem to entertainment "There's No Business Like Show Business" that was used in the movies Annie Get Your Gun (1950) and There's No Business Like Show Business (1954), sung in the latter movie by Ethel Merman who originally sang it in the Broadway production of Annie Get Your Gun. The original Broadway production of "Annie Get Your Gun" opened at the Imperial Theater on Thursday evening, May 16th, 1946 and it ran for 1,147 performances.
Pebbles' third outfit, which is featured in this and later in the original series is a green shirt and a white diaper.
This marks the first appearance where Barney has black eyes instead of clear eyes.