Continuity mistake: When Lilith arrives at Frasier's, she is moving her hands, rearranging her wrap and her purse is in her left hand. Without time for her to change it, in the next shot her purse is in her right hand.
Continuity mistake: When Lilith and Frasier are in the hotel room, Frasier's shoes are on the floor by the chair, neatly arranged. When he says "that's very impressive, Dr. Sternin" and walks away, the shoes are not in the same position anymore.
Answer: In the last episode, they explained that Tossed Salad and Scrambled Eggs is a metaphor for the mixed-up people to whom Frasier dispenses his radio psychiatric advice.