When Dooley takes the dog to the hospital, he is seen placing his gun on the table at the head of the bed on which he lays the dog. In the very next scene just a second later, as the dog is being wheeled out to be operated on, the gun is back in his holster although he was never seen putting it there.
During the movie Dooley is playing a game when he is on stakeout. In the background you can see the Mustang emblem on the steering wheel. Later in the stolen police car when he is playing a game while tailing Lyman, the Mustang emblem is in the background again.
After Jerry comes out of the car wash, Dooley opens the door and water spills out but when Dooley gets into the car and leans back against the car seat, his jacket does not show any wetness when he leans forward again as he is pulling out of the car wash.