In the first shot of the film, we see the Last Will and Testament of Patrick's late father. The address listed is on West Lasalle in Chicago, Illinois. Lasalle is a street that runs north and south, there is no "West Lasalle."
When Mame is looking for a job in the newspaper want ads, right after the stock market crash of 1929, the column on the right has businesses for sale and one of them is a Radio-TV store. There were no Radio-TV stores in 1929.
Even though "Auntie Mame" takes place between 1928 and 1946, most of the clothing and furnishings are of a 1950's mid-century modern style. Telltale items are the sofas in Mame's apartment in the opening scenes, the seating that raises and lowers, and the grown Patrick's narrow lapel suit.
When Patrick and Ms. Muldoon arrive on the afternoon of
Mame's "Affair" to tell Mame that Ms. Muldoon is not the glass washer lady, Mame says, "Then I must have invited you" and takes a cocktail from Ito's tray. You hear the ice tinkling in the glass but clearly there is no ice in either of the glasses.
When Mame enters the Marie Antoinette bedroom saying "Vera, I am about to be attacked by the Knickerbocker Bank," the veil is pinned to the left side of Vera's head. A second later, it is on the right side.
When Ito passes Agnes on the staircase, as she is returning from her night out with Mr. O'Banion, he asks her "What happened Missy Gooch?" and she replies "I lived". Between the question and answer, Agnes' mink stole starts off over her left shoulder, and suddenly it is draped over her right one.
When Lindsey and Vera are waiting for Mame's return at Beekman Place after Beau's death, as Miss Gooch arrives, Vera takes off her coat and puts it in the chair by the lilies, then as Mame and Patrick arrive a minute later, Vera, Lindsey and Miss Gootch run to hide without picking up the coat, and when Mame and Patrick come in, the coat is no longer in the chair.
Patrick's father dies in September 1928. Patrick then goes to live with Mame starting on October 1. Weeks later (it's clear it was weeks, not a year), he is discovered at Mr. Page's school in the village, the same day as the stock market crash. However, the market crashed in October 1929, not 1928.
(at around 9 mins) The newspaper headline is "BUSINESSMAN DROPS DEAD IN STEAM ROOM OF CHICAGO BROKERS CLUB," but the text of the accompanying article begins "In one move, the city planning board and zoning commission yesterday both tightened and loosened restrictions on subdivision plats offered for approval."
In the final scene, Mame reads a telegram and the written telegram is filmed as it is being read. They mention the date, "June 31st". There are only 30 days in June. This is intentional. When Patrick shows up to Mame's at the beginning, Mame says that he wasn't supposed to arrive until September 31st and is then informed there are only 30 days in September.
The time line of the story is impossible. It begins with the stock market crash in 1929, when Patrick is 10 years old. We know he graduates college, and if he did so at the standard age of 21, that places his graduation year as 1940 at the earliest. The final scene is dated by a telegram as 1946, and Patrick is married with a 10 year old son. For that to happen, the story line would have to cover at least 21 years, ending, at the earliest, in 1950.
During the fox hunt scene, a puff of white smoke can be seen coming from behind a bush as the fox runs by. This is likely from a small explosion, like a firecracker, used to scare the fox along a set path.