In the opening song when Oliver sings "You are my wife," he reaches for Lisa with his left hand. As Lisa sings "Goodbye city life," Oliver reaches in and grabs her with his right hand.
In establishing shots of the farmhouse, the junk around it disappears and reappears.
The tractor Oliver drives during the opening credits is not the same one that was used in the show.
The show had a continuity error regarding how Oliver and Lisa met. A first season episode had them meeting when Oliver's plane crashed in WWII Hungary, but a second season episode had them meeting on a ship bound for Europe.
The telephone installed at the top of the telephone pole was a lineman's test set. The dial on those sets is at the top but everyone in the show is seen using it with the dial at the bottom, meaning they are holding it upside down and talking into the earpiece.