When Frasier (Kelsey Grammer), Martin (John Mahoney), and Daphne (Jane Leeves) are interviewing housekeepers, Martin mentions that when he and Frasier interviewed Daphne, Frasier thought she would steal from them. However, in "The Good Son (1993)" (the pilot episode), when Martin and Frasier interview Daphne, Frasier never mentions a fear that she would steal from them. In fact, stealing was Martin's concern about the woman they interviewed just before Daphne.
Martin Crane's card trick is the exact same as Stanley Roper's from the sitcom "Three's Company." Roper tried it on Jack Tripper in that show's Season 2 Christmas episode titled "Three's Christmas."
The title is a parody of the song "Whistle While You Work" from the Disney animated film "Snow White and the Seven Dwarfs (1937)."
Trish tells Martin that her cleaning will be like "a white tornado", and Martin defends her with Frasier by repeating the phrase. The White Tornado was an advertising campaign for Ajax Cleaner on 60s television, featuring an animated twister that escapes from the bottle and takes over a household, leaving it sparkling clean.