Friendly Freddy, the Gentleman's Tailor - S4-E30
Other mistake: Gomer and Sargent Carter buy alike suits. They are together in the suits. Gomer doesn't start sneezing until he gets to Lou Ann's apartment and Sargent Carter doesn't start sneezing until Gomer mentioned the suits will make him sneeze. (00:10:33 - 00:18:36)
Gomer and the Queen of Burlesque - S4-E21
Continuity mistake: On the company road on the base, the background changes from day to day. First there are white houses and trees, then the next day there are no houses, just trees and telephone poles. (00:09:00 - 00:19:00)
Continuity mistake: Sgt. Carter's second button down on his shirt is unbuttoned. In the same sequence of Sgt. Carter talking with Gomer, the button is done up. (00:03:00 - 00:04:00)
My Buddy, the War Hero - S1-E25
Continuity mistake: When the chair is karate chopped in the closeup it is completely broken. In the next full frame shot the chair is shown just without the seat. (00:08:00)
Answer: If you saw the whole series run, you know that Gomer was a country bumpkin. He fumbled, stumbled and tumbled his way into one disaster after another. There was an episode that questioned why he was never promoted. However, a few years before Jim Nabors died, the real Marine Corps, gave him a ceremonial promotion to the rank of Lance Corporal, which Jim gladly accepted.
Unfortunately, I never saw all the episodes. Only a few episodes and a clip of the episode where he sings "The Impossible Dream" which made me wonder why he was still a PFC. Thanks so much for the info.