The Coca Cola bottles used as props in the lunchroom scene are modern bottles, with a red rectangular label and the familiar Coca Cola script trademark in white lettering. Period Coca Cola bottles were typically smaller (6 oz.) and the label was simply the trademark white lettering imprinted on the bottle (no red background).
In 1963 Albert Duhamel, host of the book review show I've Been Reading, is shown requesting several renowned authors as guests for his show, among them Ernest Hemingway. Ernest Hemingway's well publicized death occurred in July 1961.
When Alice Naman is calling different TV stations across the country in an attempt for them to carry "The French Chef", one of the stations on her list is WYCC, which was one of the PBS stations in Chicago. Additionally, she mentions that the Kennedys are in the White House, which places this scene in or before November 1963. The station that was to become WYCC wasn't founded until 1965, and it didn't use the call sign "WYCC" until 1983.