When the blinds are pulled, they are inside the window. After Earl crashes through the window, the blinds are on the outside of the window.
Walter Burns visits a Balaban and Katz theater while it's showing a Universal Newsreel. Paramount controlled the Balaban and Katz chain, so it would've shown a Paramount Newsreel.
The silent version of The Phantom of the Opera (1925) is playing at the Balaban and Katz. In 1929, Universal reissued the movie with a music and effects track, and a Balaban and Katz theatre in Chicago would've been equipped for sound by then. If the silent version was to be played, Peggy Grant wouldn't have stepped away from the organ console after "Button Up Your Overcoat." After the newsreel, she would've started accompanying the feature presentation.
Hildy reminds Jenny, the cleaning woman, that he got her husband on The Amateur Hour. Major Bowes' Amateur Hour premiered as a local show in New York in 1934, and on the NBC Network in 1935, six years after this movie was set.
The girls at the mayor's favorite cat house know him as The Green Hornet, after the radio superhero. The Green Hornet first aired in 1936.
When Hildy enters the press room to say goodbye to his fellow reporters, he greets them with an Edward G. Robinson imitation, saying "This is a raid, see." Robinson wasn't famous enough to imitate as a "gangster" until Little Caesar (1931) came out two years later.
Before Walter first meets Peggy at the movie theater, he tears a star off a poster for All Quiet on the Western Front (1930), an "old" movie that had not yet been made in 1929.
Earl Williams is scheduled to be hanged in June 1929. In 1928, Illinois changed its executions from hanging to electrocution.