Gomer, the Beautiful Dreamer - S4-E5
Continuity mistake: Sgt. Carter and Gomer arrive at Miss. Bunny's in Sgt. Carter's red car, but Sgt. Carter's red car was demolished by a wrecking ball in Season 2 Episode 13: Gomer Minds the Sergeant's Car. (00:07:47)
Supply Sergeants Never Die - S2-E6
Continuity mistake: The Supply Sergeant Singer's second shirt button is buttoned as he approaches the counter, but as he continues around the counter it's not, then it's buttoned up again. (00:25:00)
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)
Gomer and the Queen of Burlesque - S4-E21
Continuity mistake: Gomer is on a date - they come out of the movie theater and it's dark. Back at the base after his date Gomer runs into Sgt. Hacker, and it's daylight and the sun is shining. After their brief conversation Gomer tells Sgt. Hacker good night. (00:07:00 - 00:08:00)
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.