Continuity mistake: "Night of the Bubbling Death": When Grigsby first approaches the stolen U.S. Constitution, it's under glass (we can see the light reflections). But seconds later he lifts the paper without removing the glass, which has disappeared. It's back later, when West must cut it to retrieve the document. (00:09:10 - 00:36:30)
Factual error: The small round table in West's railcar parlor has a flip-over top, with secret maps hidden on the underside. The wine decanter and glasses all stay attached when it flips. But impossibly, when West turns the tabletop back over at the end, there's a full cup of coffee sitting on it. (00:48:30)
Revealing mistake: "Night of the Bubbling Death": Artemus takes off his coat and is wearing smoke canisters strapped to his back underneath. But the close fit of his jacket in previous shots reveals that the device wasn't there until just before he began removing the coat. (00:43:15)
Revealing mistake: "Night of the Underground Terror": During the climactic fight scene, James West's famously tight trousers rip apart in the crotch, amply revealing his very 20th-century white jockey briefs. A few shots later, that rip mends itself and the pants are split (much more decorously) down the right outer seam instead. (00:46:00)
Continuity mistake: Halfway between the opening credits and first freeze frame, Gordon and Ms. Lily Fortune are seen entering the private train car in the dark of night, but the shot before their entrance is of the front of the private train car at twilight. That shot of the train car also shows a backwards number 3.