When Mr. Drysdale and Jane are first seen driving, the wall to the right of them is somewhat dark, has various-sized rock bricks and has big bushes scattered along it. They can be seen driving uphill, and the wall is constructed in that manner. Then when they show the close-up shot of them talking, the wall has changed to a white painted cinder block type of wall with no big bushes, and they are driving at a downhill angle from its construction. Then when they see the signs along the side of the road, the wall has changed back to the first style of bricks with the bushes, and they are driving uphill again.
When the butler finds Cousin Bessie in the chandelier, she is wearing a different dress than earlier. She also has a bonnet and no tights or shoes. Jethro takes her down per the butler's order. When Jed comes in, the four of them are seen chatting and Jethro is holding the chimp in his arms on the left side of his chest, but when they switch to a close up of just Jethro and Elly, the chimp is being held on the right side of his chest.
Perhaps more of a difference than a mistake, but last week's show had Cousin Bessie in just a dress and diapers. This week she's also wearing tights and shoes.