A Little Chicken Soup Wouldn't Hurt - S5-E10
Continuity mistake: While Molly empties all the homemade food from her black bag onto Carter's desk and then the men eat, Molly's purse is either hanging from her left arm or it's gone, depending on the camera angles.
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.