Opie's Job - S6-E1
Visible crew/equipment: When Goober walks up to Andy outside the grocery/meat store, before Goober picks up the apples we can see a chalk mark on the ground between his feet.
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.
Opie's Job - S6-E1
Continuity mistake: When Aunt Bee walks by Floyd's shop the barber's pole is missing, but when Opie and Billy run across the street there's a red/white striped barber's pole, then when Andy walks by Floyd's shop the barber's pole has red/white/blue stripes.
Opie's Job - S6-E1
Continuity mistake: We see the exterior of the grocery/meat store a few times during this episode, and there are differences in things such as the actual facade of the building, the view through the doorway, etc.
Opie's Job - S6-E1
Continuity mistake: When Opie and Billy are both heading to the grocery store to apply for the job, the church is behind the boys and they're standing in front of the 'new and used furniture' store - both of which are to the right of the courthouse (when facing the courthouse), and to the left of the courthouse are the barbershop and the grocery/meat store.When the boys run across the street, they're coming from the opposite direction.
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.