When Ray jumps down from the top of the garbage truck after shooting through its windshield from above, we clearly hear the sound of his gun hitting the ground, but when he pops back up to approach the truck from the front, the gun is in his hand.
When Danny drives Julio's Mercedes from the impound lot, it has an obvious rear-view mirror on the windshield. In the close-up of Danny and Ray in the vehicle afterwards, the mirror is not there. In subsequent shots, the mirror is sometimes there and sometimes not there.
When Hughes reports that their taxi, chasing Julio's limo, is heading south on I-190, you can see them pass the exit for the Hyatt Regency O'Hare. However, they exit at River Road (north), and you see the Hyatt again on the off-ramp. Right afterwards, once you see them exit onto River Road, the scene suddenly shifts to Oakton Street and Niles Center Road in Skokie. The two locations are 9 miles apart and would require driving through the towns of Des Plaines, Park Ridge, Niles, and Morton Grove first.
In the scene in which Gregory Hines and Billy Crystal are discussing their shooting accuracy at the get away vehicle with the men who tired to rob them after they first arrest Snake, Hines' character says he hit the windshield with all six shots. However, there are only 5 bullet holes in the windshield.
At the start of the Limo chase, as the limo pulls away from the airport a white Ford Mustang pulls out in front of it (as seen from the limo.) The next shot shows the Limo strike a white Plymouth Horizon.
The film takes place around the Christmas season, as suggested by the 'snow' seen in all of the street scenes. However, it is painfully obvious the snow is nothing more than soap bubbles that has been haphazardly blown across the street, vehicles, and various structures. The most glaring example of this 'fake snow' effect is when the two lead actors go to Aunt Rose's funeral. The trees and headstones look like they've suffered a bubble bath fight, rather than a typical Chicago snowstorm.