Near the beginning of the film, in the cocktail lounge, Linda lowers the glass from her mouth three times between shots when she notices Tom at the bar.
Tom Alder and Linda Foster are at dinner and invite Leroy Dane to join them. When Dane sits down Linda's right hand is obscured by the floral centerpiece. Cut to a two shot of Linda and Dane and her martini glass is raised in her right hand.
The plot consistently uses pediatrician for the doctor who might have treated the missing girl. Yet, obviously if she were pregnant it would be an obstetrician she would have been seeing.
When Tom is in the newspaper morgue and finds the article missing, he refers to it as page 4. However, he is looking on the right side (recto) of the newspaper. Even numbers would be on the left side (verso).
Shown through the plane's windshield, a fly lands and doesn't get blown off.
When Tom calls Chevy Chase, Maryland at three o'clock in the morning, the minute hand on his bedside clock isn't moving.
According to the dialogue, Doris Delaney disappeared twelve years earlier. The movie is set in 1961, as mentioned at the beginning by a title card that says "Hollywood 1961." Yet every account of Doris' disappearance gives the year she disappeared as 1947, 14 years earlier.
References to a particular day's newspaper item are repeatedly stated by page number, section number, column number. The more usual order to give that info would be section number, page number, column number.
In the newspaper, the missing article on the page is only a small portion of column 3. Without describing where on the column, others know exactly which part of the column is missing.
Tom, an experienced investigator, should have immediately recognized a woman he was intimate with only ten years earlier in spite of her new hair color.