The license plate on Hollywood's car had Pennsylvania over the list of Bad Girl. A real Pennsylvania plate at the time (1986-1987) would have had You've Got A Friend In above and Pennsylvania below the plate ID. It also would have only been on the back of the vehicle.
During the chase scene at the end of the movie, Switcher can be seen wearing white sneakers as he runs down a flight of stairs. But in the rest of the chase scene he is wearing the bowling shoes he has on during the rest of the movie.
Right after Hollywood tells Switcher that all the girl mannequins are gone. The following shot shows Switcher in the display window where Emmy was and there is still a girl mannequin in the display window.
When Felix and Mr. Richards chase Jonathan and Emmy on Jonathan's Harley, the car that the two men are initially sitting in is black but in the next few shots it is a completely different color - a bright green.
Towards the end of the movie, Hollowood holds off several security guards with a fire-hose, hosing them down and completely soaking them for at least 5 minutes. However, when the water is turned off and the guards burst into the store room, all their uniforms are dry and many appear to be freshly pressed.
The goof items below may give away important plot points.
In the end chase scene at the department store, Roxie comes out of the storage room with the trolley of defective mannequins. You will notice at the back of the trolley as it comes out of the door a mannequin with both hands in the air and a purple outfit, it also has a head. In the very next scene as Roxie just enters the compactor room, look to the left and you will notice that that mannequin has switched to a headless mannequin and the arms are not in the same position, but it's still dressed in purple.
Emmy is only a mannequin when there is someone (other than Jonathan) around to see her. The trash compactor room is empty when Roxie comes in to destroy the mannequin; there seems to have been plenty of time when Emmy was left unattended that she could have reanimated and escaped.