The two cops near the beginning are in a blue Chevy sedan. When they pull into the alley, they are in a green Plymouth.
During the initial response to the robbery and subsequent pursuit, the red dash light on the Cadillac changes location and is inconsistently on or off.
When the radio call goes out for the liquor store robbery, it says it's at "Moulson Liquors". The sign on the store says "BF Liquors".
The radio says the liquor store robbers are traveling south on Superior Street. The real Superior in Chicago runs east-west.
After the shack blows up and almost kills Sidney & Hooker, Captain Capkowitz says they need to call a coroner. There'd be nothing for the coroner to examine. The body would have been disintegrated (or at least cremated) in the explosion.
During the truck pursuit, the first police car is a stunt vehicle, as it has red and blue overhead lights and only says "Police" on the side. It was crashed shortly after it was shown. The other Chicago police cars had all blue lights and said Chicago Police on the side.
Even though Chicago Connection is supposed to be in Chicago almost everyone has a New York accent.
After Hooker is made as a cop, the two gun thugs fie more rounds than their guns can hold.