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 died at age 39 in 1971 and 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).