The movie theatre where Don runs into Peggy is showing Casino Royale (1967) - the Ian Fleming 'James Bond' novel that the Albert R. Broccoli did not have the film rights to and was made into a comedic feature film. This is evident from the distinctive Herb Alpert and the Tijuana Brass score. Meanwhile, the closing of the episode is accompanied by 'You Only Live Twice' - the theme song to the 5th Bond film - Broccoli produced - of the franchise, also released in 1967. 1967 is widely considered to be the zenith of Bond (and secret agent / spy) 'fever'in popular culture.
The man and woman at the bar are played by husband/wife Al Jean and Stephanie Gillis. Jean is the long-time showrunner of The Simpsons (1989), and Gillis has written several episodes of that series.
Elisabeth Moss (Peggy Olson) & Alexis Bledel (Beth Dawes) also worked together on The Handmaid's Tale (2017) as June Osborne & Emily respectively.
Although credited, January Jones (Betty Francis), Jared Harris (Lane Pryce), Kiernan Shipka (Sally Draper) & Christopher StanleyChristopher Stanley (Henry Francis) do not appear in this episode.