Norton's "Call me Eduardo" was an ad-lib. The script said "Call me Edward."
Because Charles Korvin (Carlos) couldn't dance a step, he arranged to take lessons after he got the part. Nevertheless, what he's doing looks nothing like the mambo.
The title refers to the 1954 song "Papa Loves Mambo," written by Al Hoffman, Dick Manning, and Bix Reichner. The best-known recording was made by Perry Como, which topped the charts at #4.
Carlos Sanchez was largely modeled after Caesar Romero, who was actually considered to play the part.