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.