In this episode, the employees are clueless as to what Mrs. Slocombe's first name is. However, she reveals her first name in the pilot episode when she tells Captain Peacock to call her "Betty". It's assumed this was an intentional overlook by the writers to add extra comedy to the episode.
The trivia items below may give away important plot points.
When everybody is allowed to have a look at Mrs. Slocombe's present, they only look at it while it's lying in its box and it is never actually shown to the TV audience. Then, Mr. Humphries breaks the fourth wall by directly addressing the audience, saying "We're not going to tell you what it is, it's a secret!"