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)
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)
Friendly Freddy, the Gentleman's Tailor - S4-E30
Other mistake: Gomer and Sargent Carter buy alike suits. They are together in the suits. Gomer doesn't start sneezing until he gets to Lou Ann's apartment and Sargent Carter doesn't start sneezing until Gomer mentioned the suits will make him sneeze. (00:10:33 - 00:18:36)
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: 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