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)
Friendly Freddy, the Gentleman's Tailor - S4-E30
Continuity mistake: Gomer's suit has one button but after he has the suit dry-cleaned the suit shrinks and gains a button to be a two-button suit. (00:09:36 - 00:17:43)
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)
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)
Continuity mistake: Sgt. Carter's second button down on his shirt is unbuttoned. In the same sequence of Sgt. Carter talking with Gomer, the button is done up. (00:03:00 - 00:04:00)
Answer: There's no indication they were meeting for the first time, in fact they seem to know each other as Sgt. Carter addresses Andy only as "Sheriff". Gomer Pyle just says his two favorite people are "meeting face to face", and obviously in the pilot episode Sgt. Carter wasn't one of Pyle's favorite people yet.
Bishop73