The Burgie Beer billboard seen along Highway 6 is out of place, as it had long been established that Mayberry was a dry county, except for what the moonshiners provided, of course.
When when the motorcycle pulls away from the sidecar, it is clear that it's not Barney driving, but a stunt double. As the motorcycle comes back to the sidecar, the double can be seen again briefly.
When Barney is at Checkpoint Chickie warning truckers, he's seen twice on a highly-traveled, multi-lane thoroughfare. As Barney approaches a truck, the camera pans too far and it's a four-lane road, with a Burgie Beer billboard on the other side of the highway.
When Barney is on his motorcycle, marking tires and turns a corner, the camera reveals a set of street car tracks in the middle of the road, a public works feature that would not have existed in a small town such as Mayberry.
The Quonset huts from the "Gomer Pyle: USMC" set can be seen in the background of the final scene, when Andy pulls over the half-track on "Highway 6."
Barney's safety goggles do not have lenses.
Highway 6 is never again mentioned in the series, which is strange since traffic noise on the highway is audible in Andy's house.
The episode time-setting is 1964. The flags on Barney's motorcycle are 48-star flags. The 48-star flag was replaced in 1959 by the 49-star flag and in 1960 by the 50-star flag.
The flags on Barney's motorcycle have only 48 stars. The 50th star was added in 1960. The show aired in January, 1964.
When Barney pulls away on the motorcycle, leaving Andy behind in the sidecar, 14 blocks of wood are visible holding up the sidecar.