When Oscar and Harvey are in the movie theater, they talk about the canon of Rock Hudson/Doris Day movies. Tony Randall co-starred with Hudson and Day in those movies.
Oscar's wearing a New York Yankees cap, although he'd wear a New York Mets cap exclusively going forward.
When Oscar walks into the Beekman Theater, the marquee reads: "Academy Award Winner Best Foreign Film". In 1970, it was Investigation of a Citizen Above Suspicion (1970).
The title references the musical stage play, I Do! I Do!