When the car's steering breaks as it's crossing the rickety bridge and then spins out of control, you can hear the screeching of tires. Since the car was not on a paved road but a muddy backwoods dirt road, the tires would not have screeched.
When the mechanic is working on the car, he removes a piece of metal from the blacksmiths forge. The fire is much too low and burning too slowly to heat metal to the red hot state needed for forging.
Jenny refers to it being November, but the calendar in the general store shows January (1960). It could however be that the calendar simply wasn't changed from month to month.
As Buz and Tod are discussing being lost from Route 66, they mention heading to the Gulf Coast. A route from New York City to anywhere on the Gulf Coast would not be on or cross Route 66 as it stretched from Chicago, through St. Louis, Oklahoma City, and others, to Los Angeles.