When Matthews leaves the roadblock to chase the fleeing criminals, he is driving a 1957 Buick. In the next wide shot showing the pursuit, the patrol vehicle is a 1958 Dodge. As Matthews pulls up behind the suspects parked on the side of the road, he is back in the 1957 Buick.
Mathews leaves the crime scene at Eugene's Jeweler completely unattended by any law enforcement/coroner/crime scene personnel.
When Joe exits the car to go into the store with the old man, there's a stopped 54 Oldsmobile coupe in the middle of the road that begins to accelerate as the camera picks it up. The stopped reflection is also visible across the street in the windows,
When Joe gets to the road looking for a ride, as he looks to his left down the road, a truck can be heard to start or be put in gear and accelerate towards Joe. First he looks to his right for no reason as the direction of any vehicle would be going in the opposite direction he wanted to go.
After Anita's car is inspected at the road block, she and the officer walk away from the trunk and leave the trunk key in the lock. Anita gets in her vehicle, starts the car and is allowed to drive on. Side note: In that era some automobile manufactures use the same key for the ignition and trunk.
Charles Alden [the furrier] says, "Mr Mathews..." However, at no point did Mathews introduce himself by name, nor did the patrolman refer to him by name.