Herbie Faye (William Dunn) previously appeared in a different role in Fastest Gun on Madison Avenue (1966).
The title comes from the expression "a bum rap" which is defined as a false accusation.
The "Dilliway and Dunn" setup, especially with the "Positively, Mr. Dilliway" "Absolutely, Mr. Dunn" is a tribute to a real vaudeville duo from the 1920s-Gallagher and Shean. They had a hit song that was typical of vaudeville acts. Each verse ended with a question-and-answer refrain, one of which - "Positively, Mister Gallagher? Absolutely, Mister Shean!" - became a well-known catchphrase for many years thereafter.
A plastic baby doll is substituted for Tabatha when Samantha put her in her crib as she talks with uncle albert in the nursery.