Opie's Job - S6-E1
Other mistake: In the scenes outside the grocery store with Mr. Doakes, there are a couple dozen cereal boxes in the display windows - Post Grape Nuts, Post Grape Nuts Flakes, Post Alpha Bits, etc., and all the boxes have part of their names covered, such as "Rap Ut." It's pretty funny considering that TAGS cast did commercials for Post Grape Nuts, and other Post foods.
Other mistake: In this episode (aired Sep. '64) Barney tells Andy that 5 years ago on May 16 (1959) he joined the sheriff's office, and later they all have a surprise party for Barney. However, in season 4 "Citizen's Arrest" (aired Dec. '63) Andy tells Barney that he found, "The custody receipt for the first revolver I issued you... August, 1953... 10 years ago last month since I swore you in." Andy even mentions having a party with a cake that has 10 candles on it.
The Barbershop Quartet - S7-E3
Other mistake: At the end of the show Andy talks about the upcoming bowling league. Howard shows Andy his injured left thumb. This should not affect his bowling since Howard is right handed.
Other mistake: Opie accidentally drops and breaks the bottle of perfume and doesn't realise it's colored water, a bottle of perfume would smell for days.
Other mistake: In some episodes Barney can sing beautifully, but in others he can't sing at all.
Aunt Bee Learns to Drive - S6-E21
Other mistake: Aunt Bee says that Andy had to drive her to Clara's and Andy says it's not a bother, but Clara has always lived right next door.
Other mistake: During the scenes at Elmo's shop, where Aunt Bee's pictures are developed, it's obvious that this is actually Emmett's Fix-It Shop. We can see the window of the shop next door through Elmo's doorway, and recognize it as the store next door to Emmett's shop which has "Furniture, New and Used" on its front window.
Other mistake: Twice during the episode the actor who plays Floyd is replaced by his body double. The first time is when Floyd's driving to and away from Wally's station in the earlier scene, and the second is later, when Aunt Bee leaves Floyd's shop and we see Floyd stand up through the window.
The Statue - S7-E23
Other mistake: At the end of the ceremony, when Aunt Bee finally unveils the life-size statue of Seth Taylor the prop jiggles (presumably it's plastic) back and forth on the base, even though we know it's carved out of a block of granite (stated by Howard earlier in the episode) by a stonemason. (00:05:00 - 00:22:55)
Andy's Old Girlfriend - S7-E20
Other mistake: At the cabin, when Andy and Alice are fixing breakfast at the kitchen counter, note the cereal box's brand name is covered (presumably painted), which is still recognizable as "Post Toasties." (Andy Griffith even did commercials for this specific cereal). (00:20:00)
A Visit to Barney Fife - S7-E18
Other mistake: After Andy and Barney hear on the radio that another supermarket has been robbed they head over there, and in the shots at the supermarket note that many of the products on the shelves have their brand names covered with tape or scribbled over. For example, boxes of "Mrs. Cubbison's" stuffing/dressing and "Sunshine Cheez-It" are covered with tape. (00:16:40)
Other mistake: Twice during the episode there's a brick wall adjacent to the grocery store which should not be there. First when Clara walks down the street toward Floyd, then later when Andy and Opie also walk down the street toward Floyd. (Shot in the studio not backlot). (00:02:05 - 00:16:55)
Three Wishes for Opie - S5-E14
Other mistake: When Barney uses the gypsy lamp and cards in the back room, in the shots with Goober and then with Opie while they're standing in the doorway, the wall opposite them has a barred window, but in earlier episodes that wall has the door that leads outside to the side of the building.
Other mistake: When Andy and Helen are in the squad car alone after going to the movies with Gloria, both car doors are closed, but in the closeups from outside both sides of the car, note that both triangular vent windows are missing and we can see the doors' rubber seal - both doors are open for these closeups.
The Case of the Punch in the Nose - S5-E25
Other mistake: In the shots from outside the courthouse, when the front door is opened there's a wall where none should be, presumably to prevent seeing inside the courthouse facade.
Other mistake: After the preacher walks past Andy and Sam, when the two men comment that the preacher's sermons "go on" and are "dry as dust," we can tell that all of the store's glass window panes have been removed, presumably to avoid the crew/camera's reflections as the shot pans across the window to Howie.
The Arrest of the Fun Girls - S5-E28
Other mistake: When Andy, Helen, and Thelma Lou are parked in front of the courthouse the lights turn on, and in the closeups from outside both sides of the car, note that both triangular vent windows are missing - the two doors are actually open for these closeups. This happens again later, when Andy and Barney are each apologizing individually to Helen and Thelma Lou.
Aunt Bee's Invisible Beau - S5-E27
Other mistake: After Andy talks to the butter and egg man in Mt. Pilot, when Andy gets in the squad car with Barney all the car doors are closed, but in the closeups from outside both sides of the car, note that both triangular vent windows are missing - the two doors are actually open for these closeups.
Opie Flunks Arithmetic - S5-E30
Other mistake: When Aunt Bee walks out of the grocery/meat store the door's located between the grocery's one display window and the TV display window, but the grocery store actually has two display windows with its door between the two. This was shot on the soundstage, not backlot.
Andy's Rival - S6-E2
Other mistake: After Helen calls Andy to cancel their date, it cuts to Goober and Andy walking down the street and there's a brick wall adjacent to the grocery/meat store which should not exist.
Answer: It was a joke. They were supposed to be dumb hillbillies.
Both. According to later interviews with both Andy and the Dillards band (the real name of the band that played the parts of the Darling children, of which Charlene (Maggie Peterson - Mancuso was also a member) the reason the Darling boys never had any lines was because they would've had to have been paid if they spoke. In return for appearing without lines or pay, Andy promised to get as much of their music onto the show as possible which, he did. This obviously gave them a lot of exposure.