Other mistake: Private Gilbert "Duke" Slater's name is not on the back of his USMC sweatshirt like the other Marines. On the back of sweatshirt is the name Estin HP not Slater G. (00:17:00)
A Date for the Colonel's Daughter - S1-E10
Other mistake: The Colonel has his officer insignia on his shirt collar with a tie during the day while at the office. Later at home, he is in full uniform with tie and jacket, and he doesn't have his officer insignia on his shirt collar. (00:01:00 - 00:11:00)
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.