Continuity mistake: "Night of the Bubbling Death": The dust left on West's jacket after the fight changes patterns several times, then disappears altogether when he enters the building. A shot of his feet shows us that his formerly dusty boots also polished themselves. (00:04:00)
Continuity mistake: "Night of the Arrow": President Grant's cigar keeps getting longer, shorter, and longer again as he gives West and Gordon their special assignment aboard the train. (00:08:10)
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)
Continuity mistake: "Night of the Arrow": When Artemus pours the president a drink, the glass is only 1/4 full. When Grant picks it up, however, it's suddenly 3/4 full. (00:09:15)
Continuity mistake: "Night of the Bubbling Death": Artemus tosses just one bottle grenade at the pursuing posse of bad guys. In the next shot, however, multiple explosions go off all at the same time in a straight line across the road. (00:14:00)
Continuity mistake: "Night of the Bubbling Death": West uses a glass cutter to retrieve the US Constitution, which was lying flat under a covering sheet of glass. But when he reaches in and pulls the document free, it is no longer flat, but is rolled up. (00:36:15)
Continuity mistake: "Night of the Arrow": West and Gordon leave two champagne bottles and four glasses sitting on the table when they walk away to answer the door. When they return, the bottles and glasses have all completely changed positions by themselves. (00:41:30)