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)
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)
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