Continuity: While Frasier and Niles are having coffee outside at Cafe Nervosa, a red napkin is by Frasier's cuff. In the next shot it is suddenly in the center of the table, even though no one touched it.
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Quotes
[Martin sees Frasier has a lot of cuts on his face from shaving.]
Martin: I thought you were just going to slit your wrists. Looks like you went for death by a thousand cuts.
Frasier: I cut myself shaving because I was shaving without water. Why was there no water? Because I had to move your chair, which gouged the floor, which made me call for Joe, who found bad pipes, which called for Cecil, who ate the cat that killed the rat that LIVED IN THE HOUSE THAT FRASIER BUILT!!
Trivia
At one stage, Niles refers to Frasier's 'Big red clown shoes'. Kelsey Grammer provided the voice for Sideshow Bob in The Simpsons, a clown character who wore such shoes. In fact, in the first episode Kelsey Grammer's voice was used, those shoes were key to the plot. See more...
Frasier (1993) - 1 mistake in "My Coffee with Niles"
starring David Hyde Pierce, Jane Leeves, John Mahoney, Kelsey Grammer, Peri Gilpin (add more)
Updates: 
Series 10
My Coffee with Niles (season 1, episode 24)
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