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.
Jeannie, the Hip Hippie - S3-E6
Factual error: At the end of the episode, Major Nelson leaves his Cocoa Beach, Florida, house and drives down the street. Behind the house at the end of the street (which is the home used for the Stephens family on "Bewitched"), there is a mountain. There are no mountains in Cocoa Beach.
Factual error: We see how the accident-prone Wilton Parmenter was a soldier at Appotomatox during the Civil War when he sneezed. Union soldiers mistook his sneezing for a call to regroup and charge, winning the battle. Wilton Parmenter was awarded the Medal Of Honour. Accident-prone, even in his moment of glory, when the medal was pinned on Wilton's chest it pierced his skin, drawing blood. Wilton was therefore awarded the Purple Heart, becoming "the only soldier in history to get a medal for getting a medal." This was not possible, for the "Purple Heart" (or "Badge Of Military Merit", to use its proper title) awarded to US soldiers wounded in action, was only instituted in 1932. (Before somebody corrects me, George Washington did institute the award for some distinguished combatants during the War Of Independence, but it was never awarded during the nineteenth century, and revived in 1932).
Maxwell Smart, Private Eye - S3-E5
Factual error: A revolver generally only holds six bullets, but 99's gun fires way more without reloading at any point.
Visit to a Hostile Planet - S3-E2
Factual error: On the MTG radio broadcast the announcer states it is 3:15am on Saturday, 17 October 1947. 17 October 1947 fell on a Friday.