Both the insurance investigator and the sheriff assume that the recovered 9 mm Luger bullet had been fired by a German Luger pistol. In fact, there were several pistols in the 1940s that fired the 9 mm Luger cartridge, among them the Luger pistol, the Browning Hi-Power, and the Walther P-38. Even a ballistics expert couldn't determine the make and model of a pistol by merely glancing at a spent bullet with the naked eye.
The vehicle used on the street is not the same vehicle used for close-ups. The first vehicle has a chrome horn ring and plaid seats. The one used for close-ups has no horn ring; the seats are a mix of plaid and solid colors.
The insurance investigator assumes from the smell of the barrel that various pistols he encounters have been fired recently (a common Hollywood mistake). Once the smoke of a shot dissipates (within minutes), all that even an expert can determine is that a gun has been fired since it was last cleaned - whenever that might have been - not how recently it had been fired.
When Sam first calls his boss Blakely about the case, Blakely says he hopes the insurance beneficiary is the killer because then the company won't have to pay off on the policy. That's incorrect. The company won't pay the killer, but the benefits will be paid to an alternate beneficiary or perhaps to the dead man's estate.