When Ruth Gordon won her Best Actress in a Supporting Role Oscar for Rosemaries Baby (1968) in April 1969, she was asked backstage by the reporters if Mia Farrow was upset at being overlooked for a nomination in the same film. "Nahhh," Gordon replied. "Besides she'll win it next year for John und Mary (1969)." But Farrow was snubbed for this film as well, and in fact never received a nomination in her decades-long career.
The magazine in Mary's apartment which John is seen reading is the quarterly British film magazine "Sight And Sound"; it is the Winter 1968/1969 issue. While this was the latest issue at the time of filming, it is perhaps not a coincidence that it contains a detailed and highly laudatory article about Rosemaries Baby (1968), starring Mia Farrow, and a rave review of Bullitt (1968), directed by Peter Yates. A later issue of the magazine praised "John And Mary", too.
The original novel is set in London and features exclusively British characters. The first several versions of the screenplay by John Mortimer retained these settings and characters, but Peter Yates was unable to set it up as a British film, and so the script was rewritten for New York characters and settings. However, Mortimer was kept on for these rewrites; it was his only screenplay for an American-made film.