When Mary takes the coins from Bert she reaches out with her right hand, but the close-up shot shows her holding them in her left hand.
After Stack has been killed, the blood patterns on Smoke's shirt continue to change throughout the rest of the movie as long as he is wearing it.
The opening narration mentions people who have "the gift of making music so true, it can pierce the veil between life and death, conjuring spirits from the past and the future," mentioning the Irish filidh and Choctaw fire-keeper. Neither of these are musicians. The filidh was a composer and reciter of poetry; playing music was a separate and less prestigious occupation. The fire-keeper tends a sacred fire at ceremonies.
The background music, "Juke," by Little Walter, was from 1952, and "Wang Dang Doodle," by Howlin' Wolf, was from 1961. Neither work was typical of 1932.
When Smoke and Stack are waiting for Hogwood early in the movie to buy the sawmill from him, they are casting notably different shadows while standing beside their car, revealing how the scene was spliced together from two different shots of Michael B. Jordan taken at slightly different times of the day.
Stack is stated to have inherited his father's guitar before he came to Chicago seven years before the story takes place. The guitar is a Dobros Cyclops, which came onto the market in 1932, the same year the film is set.
The lighter that Smoke uses to light the cigarette that he gets from Hogwood is of a modern design that didn't exist in 1932.
While a version of the Molotov cocktail was employed unsuccessfully in the 1920s, the contemporary Molotov that Grace uses in the climax would not be widespread/in documented use until the Spanish Civil War in 1936, a couple years after (most of) the film's events in 1932.
Remmick and his minions perform a rendition of the modern version of "Wild Mountain Thyme" by Francis McPeake, which was not recorded until 1957.
During the closing credits, a performance by Sammie and his band at Pearline's Chicago Blues Bar that occurred on October 16, 1992, features a Roland XP-80 synthesizer keyboard. The Roland XP-80 was not introduced until 1996. The XP series itself was not even introduced until 1994.
When Mary leaves the joint to check on the visitors, they are playing a song. Their fretting hands clearly do not follow the chord progressions heard in the recording.
So according to legend, vampires can only enter a house if invited by the owner. The Chinese woman who invited them in was NOT the owner. But the brother who was a vampire WAS an owner and the vampires could have entered.
When Mary confronts Stack and tells her she had buried her mother the day before she is wearing a light pink dress and hat. According to the customs of the era she is supposed to be wearing black.