Goodnight, Seattle (1) - S11-E23
Revealing mistake: You have to be very quick to spot this, but when the cannon goes off Niles drops the ring, you can actually see it drop between Eddie and the camera and bounce away from Eddie. In other words, it certainly doesn't go anywhere near the pate.
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.