Although Dr. Harlan Williams' (Chris Noth) military service is never specifically addressed in the movie, he is seen wearing the insignia of the 45th Infantry ("Thunderbird") Division on one of his uniforms. This unit fought in both World War II and Korea.
The movie is set in 1953, yet when Anne (Renee) is seen walking through town just before her husband shows up at her apartment in L.A. There is a car parked on the side of the road with a modern (late 90's early 2000's) New Mexico License Plate.
When the family arrives in Saint Louis for the first time, a US flag can be seen flying. However, this flag has 50 stars and in 1953 there were only 48 states.
The action of the movie is supposed to occur in the summer of 1953. In one scene a Greyhound Scenicruiser bus is shown leaving a bus terminal. The Scenicruiser did not enter production until 1954.
No. My One and Only is loosely based on the boyhood experiences of actor George Hamilton, whose mother took him and his brother on a cross-country trip in order to find a new husband. Hamilton related anecdotes related to the experience to the late Merv Griffin. The screenplay was written by Charlie Peters.