Rockford's car has four headlights before the fight on the lawn. After the fight, the car has two headlights. Arriving at the party, the car has four headlights again.
While looking in the phone book Rockford calls out a list of names, but when a close-up of the page is shown, the listed names don't match what he called out.
The baby grand piano pushed into the pool is an obvious fake. A real baby grand weighs at least 500 pounds, and would not even begin to float.
The garage where the rental car is picked up has two signs with two different spellings of 'wagon' on them (wagon, wagen).