After the tow truck arrives at the garage and all the bad guys go into the office, the emergency blinkers on the truck are still blinking. In the next shot, they are no longer blinking.
While reading the newspaper, Barney finds an ad for a 1949 Hudson Terraplane. The last model year for the Terraplane was 1938.
While returning the car, Barney and Andy break down out in the country. While being towed "after dark", there is the illusion that they are passing under numerous streetlights which would not be present out in the country.
Andy tells Mrs. Lesch it normally takes about an hour to drive from Mt. Pilot, but Mt. Pilot is only 12 miles from Mayberry.
Barney and Andy decide to return the car to the little old lady in Mt. Pilot, but they don't know her address. The newspaper ad included only a phone number, and the car was delivered to Barney at Andy's house.
Andy and Barney ride together in the "lemon" when returning the car to Mrs. Lesch in Mt. Pilot. They would have no way to get back to Mayberry.