While battling Chicago gangster Al Capone in 1931, the time travelers seek help from real-life lawman Richard James Hart, but Hart lived in Homer, Nebraska, which is over 400 miles from Chicago. He could not have covered that distance unless they let him see and use their time machine, which they evidently did not since Hart remains ignorant of time travel.
Banners meant to look like the flag of the city of Chicago are the wrong color 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.
When Connor is explaining the search capabilities when the lifeboat returns to the present, he says he can pinpoint its location with "a 50 square mile radius". A radius is a linear measurement; it'd be just "50 mile radius".