The term "Merry Andrew" is British slang for a clown.
Tickety-boo is an English term meaning 'in fine order,' or 'all is well.'
Both of Danny Kaye's leading ladies in this film eventually committed suicide - both by barbiturate overdose. Pier Angeli at age 39 in 1971. Patricia Cutts at age 48 in 1974.
The first section of the film is set on the oft-used Tait College portion of the M-G-M backlot, most famous for its appearances in Best Foot Forward (1943) and, especially, Good News (1947). It would also feature prominently two years later in Where the Boys Are (1960).