Steven Spielberg was just 24 when he helmed this episode. He had to be approved by Peter Falk before being allowed to direct. The two had a meeting beforehand and Falk was immediately won over by the young director's enthusiasm.
The inscribed mystery novel that Ken Franklin gives to Miss LaSanka is titled "Prescription: Murder", the same title as the first Columbo movie, Prescription: Murder (1968).
Lilly LaSanka states that she was taught to cook by her husband, who was a cook as a merchant marine. This is an in-joke as being a cook in the merchant marine was one of Peter Falk's jobs before he became an actor.
As a young director, Steven Spielberg was known for putting too much of his own style on the shows he directed, resulting in an episode that didn't stylistically fit with the rest of the series. He says he often wasn't asked back to direct further episodes because of this. Spielberg's direction reflected a stylish maturity far beyond the norm on TV for the time, but that novelty was exactly the type of direction that creators Richard Levinson and William Link wanted for their show: to look and feel more like a movie, and that made Spielberg the perfect fit to direct the series' first episode.