Factual error: The story is supposed to take place from 1965 until the baby's birth in June,1966. Yet, before Rosemary is even pregnant, there is a 1967 Chevrolet taxicab sitting at the curb. (00:36:10)
Factual error: Rosemary goes out to meet Hutch at the Time Life Building and we see the marquee at Radio City indicating that "The Happiest Millionaire" staring Fred Mac Murray and Tommy Steele is playing. The problem here is that it's already been established by the calendar on the Woodhouse's kitchen wall and by the Pope's visit it that this is winter 1965, but "The Happiest Millionaire" didn't premier until 1967. (01:10:25)
Factual error: Rosemary calls Dr. Hill from a pay phone and says, "The baby's due on Tuesday, you remember you told me June 28th" (and June 28th 1966 does fall on a Tuesday). In the previous scene in Dr. Sapirstein's office his receptionist is making an appointment "next week" for a patient and that date is "July 10th" indicating that if Rosemary is due on June 28th (which she says is next Tuesday) the dates do not match and it must still be the week of June 20th which is at least two weeks before July 10th. (01:44:45)
Factual error: One of the Cadillac limousines during the funeral scene is from 1967, but the movie is supposed to take place between 1965 and 1966.
Chosen answer: It doesn't have a specific title. It was a lullaby written for the film by Krzysztof Komeda. There's a few variations of the lullaby heard throughout the film, the opening credits version is listed as "Rosemary's Baby Main Theme - Vocal."
Bishop73