My Fair Ernest T. Bass - S4-E17
Revealing mistake: At the start, when Ernest T. throws the rock at Mrs. Wiley's window and it breaks, the area around the hole flutters in the breeze - it's obviously not a glass window used for the stunt.
My Fair Ernest T. Bass - S4-E17
Other mistake: Barney says, "I brought the car to drive you over to Mrs. Wiley's," but later when Andy, Barney, Ernest T., and Ramona leave Mrs. Wiley's we see that they're at the house that's actually next door to Andy - though to hide this fact there's a station wagon in the driveway, and they've removed the trellis beside the door.
My Fair Ernest T. Bass - S4-E17
Character mistake: During the party at Mrs. Wiley's, Ernest Bass' girlfriend is called "Ramona." At the end of the show, Ernest T keeps calling her "Romina".
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.