Gomer and the Dragon Lady - S1-E8
Continuity mistake: Sgt. Carter and two buddies are drinking beer in mugs. The "Dragon Lady" flips a man - he hits the table and knocks over a beer bottle and a beer mug on to the floor. When Sgt. Carter and his buddies go back to sit at the table all three beer bottles and mugs with beer are back on the table. (00:06:00 - 00:07:00)
Continuity mistake: The Marine Captain is showing Gomer Pyle how to salute. When she salutes she has a watch on her right wrist, but when she is shown holding the salute the watch is not on her wrist.
Continuity mistake: The length of Sgt. Carter's career in the Marines varies from 14 years to 18 years.
My Buddy, the War Hero - S1-E25
Continuity mistake: Jimbo, Sgt. Carter's buddy breaks a chair in two with a Karate chop. Jumbo prepares to chop the chair with his right hand. When the chair is shown being chopped it is done with the left hand. (00:08:00)
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.