In the opening sequence establishing the 1962 New York setting, the modern Canadian flag is among those flying outside the United Nations. In fact it did not replace the Canadian red ensign until 1965.
When Barbara arrives in NY and encounters the bomb protesters in front of what appears to be the United Nations plaza, there is a prominent shot of the People's Republic of China (PRC) national flag on one of the flagpoles. PRC did not take over the UN's China seat from the Republic of China (Taiwan) until 1971; thus, in the early '60s, the Taiwanese flag would have been displayed.
The New York City street-name signs were white-on-green, which in reality didn't occur until the early-1980s. Prior to this, the colors of the street-name signs depended on which borough of NYC you were in, and in Manhattan they were black-on-yellow.
During a conversation with Peter, Catcher refers to the Cuban Missile Crisis, which was made public in a speech by President John F. Kennedy on 22 October 1962, then later takes Barbara to a Yankees game. The baseball season ended on 16 October when the Yankees won the World Series in San Francisco.
Vikki tells Barbara that Judy Garland was a last-minute replacement for The Singing Nun on The Ed Sullivan Show. The Singing Nun was an unknown in 1962, and did not appear on The Ed Sullivan Show until 1964; Garland first appeared on "Sullivan" in 1966.
At the beginning of the movie the narration states that the year is 1962. Yet when Barbara and Catcher are "doing the town" in New York there are various titles of Broadway shows displayed, among them "Oliver!". This musical didn't open on Broadway until 6 January 1963.
The movie is set in 1962. Judging by the scenes of Barbara sunbathing, it is likely set in late spring or summer. But Catcher references the Cuban Missile Crisis and that did not occur till October 1962.
In an early scene a shot is taken of the UN building showing the flags from different countries. The flag for Canada shows the 11-pointed, red maple leaf. This flag was only adopted in 1964 and made its first appearance on February 15, 1965. Since this movie takes place in 1962 the correct Canadian flag would have been the Red Ensign which had a small version of the British Union Jack in the upper left hand corner and the coat of arms for Canada in the middle right-hand side on a background of red.
After Barbara finds Catch in bed at Peter's party, she runs out of the apartment to the elevator where Catch finds her and it is revealed that he is still carrying around the other woman's hat though when we see him running around in previous shots there is no sign of a hat at all.
Barbara's book is shown being bought in a Russian bookstore. The book's cover is incorrectly written using the Latin alphabet, when it should be written using Cyrillic characters. Also the title is "Nyet Lyubof", which is grammatically not correct. It should be called "Nyet Lyubvi" (in reference to the title of the book in the movie) or "K chertu lyubof'" (in reference to the correct translation of the title, also the Russian title of the movie)
Early in the film, Barbara and Vikki are in a taxi discussing her interview with Catcher Block. In the next scene, Catcher and Peter are traveling in a taxi on the same street. Although the background of both scenes begin different, near the end you can see they are the same. This is made obvious by the same doorway entrance, the same woman entering her car, and the same car order in both scenes.
The goof item below may give away important plot points.
When Barbara Novak is interviewing Catcher Block as her personal assistant, Catcher shows her his exposé. Barbara says that in his expose, he had to have exposed her as Nancy Brown but earlier Peter shows Catcher the Now magazine billboard. On the billboard, the cover of the magazine is shown that says "How Nancy Brown Became Barbara Novak." Everyone knew Barbara was Nancy so it shouldn't have mattered if Catcher said that in his expose.