Banners meant to look like the flag of the city of Chicago are the wrong shade of blue, the wrong number of white stripes, and the wrong star style. However, the number of stars is correct, as the third star was not added until 1933, two years after this takes place.
Elliot Ness' kitchen (in 1931) has a fluorescent light under a kitchen cabinet before they were commercially available.
While battling Chicago gangster Al Capone in 1931, the team seeks help from real-life lawman Richard James Hart - but Hart lived in Homer, Nebraska, over 400 miles from Chicago. He could not have covered that distance in that time.