Diane Keaton replaced Mia Farrow. Woody Allen had written the lead female role for Farrow, but Keaton got the part following the breakup of the pair's personal relationship. There is a rumor that, despite the very public feuding between her and Allen, Farrow showed up for a costume fitting, and needed to be informed that she was no longer in the movie.
"Manhattan Murder Mystery" was actually the generic working title during production--Woody Allen films usually have generic titles during production like "Woody Allen Fall Project"--but since no new title could be thought of, Allen decided to leave that as the title.
Anjelica Huston said that the set was "oddly free of anxiety, introspection and pain" and attributed this largely due to the presence of Diane Keaton. Huston added: "On this movie, he [Woody Allen] showed up in the hair and makeup trailer to tease Diane about her hair and her big photography books, all diligently marked with yellow stick-'em paper. Around Diane, he was open and accessible".
Woody Allen and Marshall Brickman planned to make Annie Hall (1977) a murder mystery, but cut that subplot out and used it for this movie. This is why Brickman is credited as co-writer.
When Diane Keaton replaced Mia Farrow, Woody Allen rewrote the script and centered the more comic side of the couple on her, admitting Keaton is funnier.