In the open, Niles and Daphne return home from a kickboxing session. It's a real-life hobby of David Hyde Pierce's as well.
This isn't the first time a mentor of Frasier's (Kelsey Grammer) has slept with a promiscuous friend of his. In an episode of "Cheers (1982)," his friend and mentor Bennett Ludlow (James Karen) slept with Carla Tortelli (Rhea Perlman). Carla got pregnant with Ludlow's child.
The first symbol card that Dr. Morey (Fisher Stevens) shows Daphne (Jane Leeves) she identifies as a star. As he lays the card down, we can see that it is actually two wavy lines.
Niles (David Hyde Pierce) and Daphne (Jane Leeves) have consulted a professional to determine if Daphne is, in fact, psychic. As an audience, however, we have ample evidence that she is. On first meeting Martin (John Mahoney), she knew he'd been a policeman. She sensed that Frasier's (Kelsey Grammer) gay boss had had a dispute with a former lover over opera records, a sensation which caused him to suddenly sit down in shock (even Frasier witnessed that). She also had a vision of her "true love" (Niles) with a dragon, and later we saw he had been given a dragon figure by Roz (Peri Gilpin). Many other visions (usually comic) also support her claim.
Dr. Morey is a professor at Seattle University, which is a small Catholic University run by the Jesuit order. (The primary university in the city is the University of Washington.)