Continuity mistake: In the opening, when Oliver goes to grab Lisa's hand, he moves his left hand. When the camera looks at Lisa, Oliver is reaching with his right hand.
Other mistake: When the phone pole was installed with a "butt set" to talk with, they used it upside down for a long time. Someone must have brought it to the director, because they finally corrected the problem.
Other mistake: In the opening sequence Oliver stops the tractor in front of the house by pulling a lever. This lever is not a brake but is to engage a wheel to put a belt around to operate a threshing machine.
Suggested correction: The lever is to engage and disengage the clutch, when he pulls it back that disengages and the tractor would stop.
Older tractors had a hand clutch like that.
Revealing mistake: Oliver and Eb cast shadows on the painted backdrop as Mr. Haney drives up.
Other mistake: A shallow tray of pancake batter is cooking on the stovetop. The coffee pot boils over and its round lid shoots into the air. Even though the lid would be extremely hot, Lisa catches it with both hands and uses it to cut four pancakes.
Plot hole: Oliver and Lisa are in a truck, taking a load of apples to the Farmers Market in the state capital. Oliver says it's a "15-hour drive." Driving 30 miles an hour, that would be 450 miles. Driving 40 miles an hour, that would be 600 miles. It was never specified where Green Acres is located but only Alaska, Texas and California extend for such a distance north-to-south and/or east-to-west.
Suggested correction: He doesn't say it's a 15-hour drive. He says it's a 15-hour trip, which could mean the drive there and back total 15 hours. Or he could be taking into account all the times they'll be stopping and traffic. Not to mention that the driving distance between two cities is always greater than as the crow flies. Two cities might be 100 miles apart but the drive may end up being 150 miles.
Other mistake: Mr. Haney is suing Oliver Douglas. While on the witness stand following a recess for lunch, Haney taps his right cheek and tells Judge Clemens, "You have some ketchup on your cheek." The Judge wipes his left cheek with a handkerchief.
Wings Over Hooterville - S2-E1
Factual error: In a flashback scene, Oliver is hanging from a tree after getting shot down in WWII. They ask him where he is from, and he says the US Air Force. The US Air Force wasn't formed till 1947. During WWII, it was the Air Corps.
The Beverly Hillbillies - S2-E23
Continuity mistake: During the spaghetti sequence there is a blue phone on the wall by the refrigerator that appears and disappears between shots.
The Vulgar Ring Story - S2-E28
Other mistake: Lisa thinks her ring went down the drain while she was washing dishes in the kitchen sink. Oliver disconnects the pipes under the sink and does not find the ring, but he removes a long blue scarf from the trap. It is completely dry.