During the final scene when Mose and Addie are driving off down a long dirt road, there's a clearly visible contrail from a high altitude plane across the sky in the distance. The film was set in the early-1930s when high altitude flights were far from commonplace.
If you watch closely, when Addie is reading the obituary of Mr. Morgan, just above and below Mr. Morgan's are two obituaries, respectively, one Bessie Lees and one Oscar G. Olsen, both entering rest on April 28th, 1971. This film takes place in the mid-30's. Also worth noting, is some of the obituaries state San Francisco as the home of a few of the deceased. This film takes place throughout Kansas and Western Missouri.
When Addie says, "Don't knock, use the key!" and sends Moze to Trixie's hotel room, we see a window behind Addie with a lace curtain. However, though this lace curtain, we can see cars that are of late 60's / early 70's style.
When Addie is listening to Jack Benny on the radio, Benny can be heard referencing his famous feud (it was a fake feud) with Fred Allen. This film takes place in 1935 but the "feud" did not start until 1937.
As Moze crosses the street in Wilson, KS to pass Addie's $20 birthday bill at the general store, the Wilson city hall building to the left of the store clearly displays a 1938 construction date, despite the general consensus that the film takes place in 1935.
The straw in the "Nehi and Coney Island" scene moves several positions during the scene. First the straw is straight and sticking out above the rim of the bottle then it's submerged then straight and above again and then leaning to the left and then back to straight again.
When Mose and Addy are agreeing to meet after they arrive in St. Joseph, he tells her to meet him on the 'Corner of East Wearing and Burlington.' There is no Wearing, (east or west) or Burlington in St. Joseph, MO. The streets in downtown St. Joseph, MO are numbered and/or named after the children of St. Joseph's founder, Joseph Robidoux.
After escaping the Doniphan County Sheriff's office in White Cloud, Kansas, Moze heads east toward the river, then turns left (north). He then realizes "the damn bridge is the other way" and turns the car around to the south. In reality the bridge they eventually cross is still further north, in Rulo, Nebraska. Furthermore, his concern about crossing the river to Missouri (to get out of the Kansas sheriff's jurisdiction) would be irrelevant if he had simply continued northbound on the highway another mile and crossed the Kansas-Nebraska border.
The film is set in 1935 and there are multiple references to bootlegging. Although national Prohibition was repealed in 1933 by the 21st Amendment, the Amendment did not legalize liquor: it left regulation of liquor to the states. Kansas did not legalize the sale of cereal malt beverage (also known as 3.2 beer) until 1937, and the first post-Prohibition legalization of alcoholic liquor did not occur until the state's constitution was amended in 1948.
Moze tells Addie that "...this particular person don't like cigarette smoke." He is referring to Trixie Delight. However, we later see Trixie smoking a cigarette when Imogene informs her of Lloyd's proposition. This apparent goof is part of Miss Trixie's efforts to create a "proper" impression for Mose; she doesn't want him to be aware that she does n fact smoke.
After Mose and Addie leave the hotel upon finding Trixie "cheating" with the desk clerk, they are driving in the rain. There is wind blowing Addie's hair and ribbon from the back, although the windows are clearly closed, as it is raining very heavily.
After Moze and Addie enter the "General Merchandise" building in Wilson, KS to pull the $20/$5 bill scam, the same building can be seen again through the window behind the cashier (with its original "Somer Hardware" sign) after Addie's "Lady, you made a mistake" line. In reality the interior scene takes place in a building on the opposite corner of the street, in the Florian Hardware building that Moze and Addie walked past after leaving the barber shop.
When the hotel clerk is writing the note to accompany the box of candy he's sending to Trixie's room, the sheet of stationery he uses has white tape over 2 areas - one just above and another just below the word "Hotel" at the top - that blocks off some type of text.