In the opening scene, the two Treasury agents are waiting inside the courthouse for the Sheriff to return. Before Opie walks in the door, the agent on the right (Rance Howard) is wearing a lighter colored suit. A second later, as Opie is walking from the doorway toward where Barney is sitting, the agents are visible, sitting in the background. Freezing the frame reveals that the two actors sitting down are not the two who entered.
Right after Gomer accidentally puts gasoline in the back of the truck, where Barney is sitting, his pants are miraculously dry seconds later.
At the beginning of the episode, the two Treasury agents come in and take their hats off. Moments later, Opie comes in and walks past them and the agents have their hats on. Moments after that, Andy comes in and their hats are off again.
At the beginning of the episode, Andy tells Barney that the two men were Treasury agents, there to set up the gold truck route. Later, when Andy is standing on the front bumper of the gold truck trying to get the crowd to disperse, he refers to them as "the FBI men." The FBI is a different department than the Treasury.
In his book, "The Boys", written with his brother, Clint, Ron Howard tells a moving story that explains that his father was a last-moment replacement for another actor. This is why there is a different actor present when Opie enters the Sheriff's Office.
Because the 40-Acre backlot had limited space for country scenes, the same stretch of unpaved road was often used for the illusion of longer distances, either shot from different angles or using the exact same footage repeated more than once. During that era of television and film making, no one expected the possibility of endless, syndicated, repeat viewings that would allow future audiences to notice these "cheats".
After Gomer pumps gas in through the gun port for several seconds onto Barney's feet, Barney remains locked in the rear compartment of the armored car while the Treasury agents come back from lunch and the truck leaves the filling station. Barney would have been overcome by the fumes in such a small enclosure with that much gas on and around him.
When Barney first gets into the armored truck, the Treasury agents hand him a Thompson submachine gun. When he's let out of the truck, the Treasury agents drive off without getting the gun back from Barney.
During the armored truck chase scene, interior shots of Barney bouncing around inside clearly show the "locked" door coming open. Also, at one point, Barney appears to kick the locked door open, but the scene cuts quickly away before a clear view is shown.
The gold truck arrives in Mayberry under rainy conditions, with most of the crowd wearing raincoats and holding umbrellas. However, when Andy leaves the gas station to chase the truck, his patrol car kicks up clouds of dust.
When Barney discovers the gold is really sand, he stands up and pounds on the window for help. The "armored" wall around the window visibly flexes when he strikes it.
The gold shipment is said to be coming from the Denver mint, in Colorado, and bound for Fort Knox, about 40 miles south of Louisville, Kentucky. There is no logical reason for the gold to be passing through Mayberry, some 500 miles further east than its destination. In the epilogue, Andy tells Barney that the real gold shipment is headed to Fort Knox via Raleigh, North Carolina, which is just as ridiculous as sending it through Mayberry.
At the end of the episode, Andy tells Barney that the plan was for the public to think the secret decoy was the real shipment. All of the extreme measures at keeping the arrival secret make no sense.
After the two agents enter and refuse to answer his questions, Barney walks over to Andy's desk. As he picks up a magazine to read, the shadow of the boom mic can be seen quickly moving down the wall behind him.
At the gas station, a big deal is made of having Barney and the armored truck guard trade places quickly so the door won't be open long. However, when the truck first pulls into town, the head FBI agent steps out of the truck through this same door and he doesn't seem worried about opening the door in front of dozens of townspeople.