Diane Keaton had just broken up with Warren Beatty, her co-star in Reds (1981). As such, she was able to draw on that experience for this role, and even gave notes to writer Bo Goldman and director Alan Parker. They weren't initially thrilled by this, but later conceded that the character was enriched by Keaton's participation in ways that they had never thought of.
The initially scheduled December 1981 release was changed in order not to hamper Diane Keaton's campaign for a best actress Oscar for Reds (1981).
For this film, director Alan Parker says that he used a technique employed by Woody Allen, of a stationery camera with actors walking in and out of the shot. Interestingly, this film's co-lead Diane Keaton had previously starred in Allen's Annie Hall (1977), which also involved the eventual break-up of the film's two lead characters.
The film's title is derived from the card game known as "Hearts", where a scoring technique in the game is known as "shooting the moon".
Writer Bo Goldman and director Alan Parker developed the film's screenplay by meeting for several weeks and talking about their respective marriages. At the time of the film, Parker was married with four children whilst Goldman was married with six.