When Frasier sees the marquee for the Jack Benny movie, he imitates one of Benny's "trademark" gestures.
The title is from the common evasion to a question: "Ask me no questions and I will tell you no lies."
A book titled "Magritte" is seen on the bookcase in the center of Frasier's apartment, just above his CDs. Rene Magritte was a famous 20th-century Belgian artist.
In "Ask Me No Questions", as Frasier is wandering the streets of Seattle, he sees a marque with Jack Benny on it. Grammer then brings his hand up to his chin and turns his head in a perfect imitation of one of Benny's trademark gestures.