The license plate on the detectives car was the old Illinois style that was no longer valid at the time this movie was produced. Also the state seal on the badges of the uniformed police officers was the state seat of California.
Nowhere in the 708 area code's geographical area (Peter's phone # on the website) are there hills as large as there are in the background at Peter's house.
As established by the external shot of Karen's BMW, she uses a novelty BMW plate on the front of her car. In Illinois one must have both front and back Illinois license plates to be street legal.