When Martin makes the joke about Frasier's being cheap, he repeats a line from his joke book: "This guy is so cheap, he could squeeze a nickel 'til the buffalo chokes." Frasier then asks him how old the book is, and Martin replies, "1956." The Buffalo nickel was minted until 1938, when it was replaced by the Jefferson nickel. Although it hadn't been minted in 18 years, many Buffalo nickels were still in circulation at that point, and people in 1956 would have gotten the joke.
Bebe explains to Frasier how she met Dr Phil "at a charity donkey basketball game...Texas darling... It's like a symphony to them." She also describes Dr Phil as "a cowboy wrapped in a genius wrapped in a dream...wrapped in another cowboy." Particularly amusing comments since Harriet Samsom Harris and Phil McGraw were born in, or have close early associations with, Texas, so the stereotypes are apt. The origin of the second quote is not lost either, referencing Churchill's famous 1939 statement in a BBC broadcast describing Russia's actions with Nazi Germany as "a riddle, wrapped in a mystery, inside an enigma."
Frasier objects to Dr. Phil on ethical grounds, explaining he felt McGraw cheated him out of gambling winnings. Not as widely known in 2003 when this aired, McGraw has since been accused of multiple serious questionable ethical practices, including presenting his advice show in a way lay audiences might regard as real therapy (actually not), practicing therapy without a license (the latter dismissed as his show was deemed as being intended for entertainment), endorsing sham health products, creating a hostile environment for both employees and guests, and racism.
Of all Seattle's downtown upscale hotels, the decor of Bebe's room is most similar to the decor of the Fairmont Olympic, which would be one of the only locations to prompt a comment from Frasier about being in the lap of luxury.