It is established that Andy and Barney graduated in 1945. However, this directly contradicts previously established facts that both Andy and Barney served in World War II. In Ellie Comes to Town (1960), Andy mentions to Aunt Bee, who is testing some perfume, that the scent reminded him of when he was in France during the war. In Quiet Sam (1961), Barney says he was stationed as a file clerk during the war.
The yearbook states Barney's name as "Bernard Milton Fife," but after Season 3, Barney refers to himself as "Barney P. Fife."
Both times Barney sings, especially at the end when it's just him and Andy, he has a perfectly good singing voice. He does not sing off-key, he carries a tune perfectly and he sings nice harmonies with Andy. But in many other episodes, including the very next one, Rafe Hollister Sings (1963), he's a terrible singer whom others conspire to keep from singing in public.
Barney's full name is revealed as Bernard Milton Fife, contradicting his middle name being Oliver in A Plaque for Mayberry (1961).
At 14:00, Barney begins making a turkey sandwich on rye with his fingers. At 14:09, the scene cuts to a different camera and a fork suddenly materializes in Barney's hand with which to make his sandwich.
When Andy and Barney are looking through the yearbook, they first mention Ramona Wiley, then they continue and come to Sharon Despain. Yearbooks are arranged alphabetically. They would have had to go backward instead of forward.
When Andy and Barney each lift their end of the chest by the handle, the bottom panel presumably gives out and the personal effects lay on the garage floor. But when Andy starts to thin out the items, it's clear that there is no bottom panel, or fragments, of the chest on the floor.
As they clear off a shelf to make room for the trunk, Andy moves a box so effortlessly that it's obvious that it's just an empty prop.
At the reunion, when Andy talks to Nate Bracey (bald man with glasses) and Barney looks him up in the year book, the band plays in the background. The accordion player fingers the keyboard and buttons but isn't working the instrument's bellows back and forth as is needed to play it.
Although Andy mentions that he has a son, nobody asks Andy about a wife or if he's married. Even when he's with Sharon, no question about his marital status is ever brought up.