In a play on the usual routine for Columbo, Ruth Gordon's character Abigail Mitchell several times says, "Oh, lieutenant, one more thing." As her character is also a detective of sorts (in fact, an experienced mystery writer), this seems to fit well and the audience doesn't question it.
Columbo seems to have a "thing" for belly dancers. In this episode Columbo admires the belly dancers and is really rather distracted by them. The same happened in an earlier episode S05E03, Identity Crisis, when Columbo only half listens to his colleague, Kramer, and bar tender in Sinbad's bar whilst watching the belly dancer on stage.
This was the first Columbo broadcast when the show was on its own. The show had been one part of the wheel program The NBC Mystery Movie (1971) that rotated with Un shérif à New York (1970), McMillan & Wife (1971) (without the "and Wife" during its final season), Quincy (1976), and others. When the Mystery Movie was canceled, Quincy was made into a weekly series, and Columbo continued its 90-minute format for the 1977-78 season on its own and was then canceled. The show remained dormant until it was revived by ABC in 1989.
When Columbo finds Abigail Mitchell on the ship, she asks if he is sailing as well. He tells her that he and "Mrs. Columbo tried it once...". He is referring to Eaux troubles (1975).