Gomer and the Queen of Burlesque - S4-E21
Factual error: Gomer is a Private First Class and has one stripe. In his utility uniform Gomer doesn't have metal rank insignia on his collar. All Marines wear their rank on their utility uniforms. (00:06:00)
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.