Visible crew/equipment: While Andy's in Opie's bedroom when Opie's thinking about running away, the moving shadow of the overhead boom mic can be seen, first on the wall behind Opie's headboard and then on the door. Also note, when Andy shows Aunt Bee how to hold the baseball bat and moves her into position, we can see a long white tape mark on the grass (since it's possible that Andy placed the tape, however unlikely, it's being noted here).
Visible crew/equipment: While Andy and Barney are standing beside Bobby Fleet's vehicle, Andy mentions that it's too bad they're all not staying overnight so they could hear Jim play, and when it cuts to the next shot the reflection of the overhead boom pole and mic can be seen moving on the surface of the vehicle.
Visible crew/equipment: After Andy talks to George's father on the phone, he gets up and stands near the fireplace while explaining to Opie why he broke his promise and called George's father, and when Opie's on the couch asking if he can run off sometime, we can see the white tape mark on the rug where Andy was standing moments ago.
Continuity mistake: When Andy and Mrs. Silby are walking into the courthouse, in the exterior shot of Andy opening the door he's wearing the baseball mitt on his left hand, but when it cuts to the interior shot Andy's opening the door with his left hand and the mitt has vanished.
Continuity mistake: As Barney is turning in his deputy equipment to resign his handcuffs are hanging out of his pocket. After Barney states he wishes someone would just commit a crime, Opie enters. As the camera pans out so Andy can ask Opie what happened, the handcuffs are no longer in Barney's pocket, and he didn't put them on the desk with the rest of the equipment. (03:03:00 - 03:11:00)
Continuity mistake: When Barney and Andy are looking at Barney's picture on the front page of the newspaper, first, the article has nothing to do with Barney or the arrest, and second, when Barney takes the paper from Andy he folds it with the front page on the outside, and the page we see is not the same front page from the closeup.
Plot hole: When Barney's telling Andy about the poem written on the bank wall, Barney blames Opie and doesn't mention anything about Opie using chalk, but when Opie walks in Andy tells him, "Barney says there's a poem written on the wall of the bank, and that you were standin' along beside it with a piece of chalk in your hand," and then in a few moments Opie explains that some big kids pushed the chalk into his hands. So it's impossible for Andy to have known that chalk was used to write the poem, and not a marker, a pen, or a pencil.
Visible crew/equipment: While Barney's in the barber chair, Floyd starts talking about how he'd tried living at the back of the barber shop, and when the shot faces Barney we can see the reflection of a crew member's legs moving around - the only ones in the shop are Barney, Floyd, and the two men seated by the corner.
Visible crew/equipment: When Andy sees that several stores have made 'Hollywood' changes and then walks past the two men wearing suits, it cuts to Andy walking up to 'Hollywood funerals' and we can see the reflection of a crew member pushing the camera dolly with other crew members.