Question: Why was Bloody Mary's singing voice dubbed, given that Juanita Hall was a strong singer who had performed the role on Broadway?
Answer: Richard Rodgers was just being Richard Rodgers. He allowed her to sing in 'Flower drum Song' on stage the following year, 1958/9, and allowed her to use her own voice in the film of 'Flower Drum Song' in 1961. He had his own demons then and was just reacting.
Question: The movie was made in 1958, why does the calendar in police station show July 1957?
Answer: Because movies aren't always set in the year they're released. Absent any conflicting information, the assumption must be that the events of the movie take place around July 1957.
Question: At the beginning what was wrong with the young sailor drawing number 7 in the money draw?
Answer: Sailors are very superstitious, they considered it a bad omen. Number 7 is an area of the ocean where most ships and subs have gone down.
Answer: Richard Rogers preferred the vocal performance of Muriel Smith who played the part in London. Since the vocal tracks for musicals was recorded separately from the filming back then, dubbing occurred for many reasons other than lack of singing ability of an actor, scheduling problems, budget, etc.
Myridon