Visible crew/equipment: In the scene after the storm, the ship moves in the sand. Look at its front and you'll be able to see a wire that moves the ship. It's very visible.
Visible crew/equipment: When they're building the petticoat balloon, the camera slowly goes back. Look at the lower-right corner of the screen: there is a man wearing a stadium jacket. He's a crew member.
Deliberate mistake: Baron Munchausen sends his courier, Berthold, on a one-hour errand to procure a bottle of the finest Tokay from the imperial wine cellars in Vienna. Berthold returns with the bottle within the hour and (in one continuous wide shot) hands the bottle to Baron Munchausen, who then hands it to the Sultan, who effortlessly plucks the cork from the bottle with his fingertips and pours a glass for himself. But there is no way the Sultan could simply pluck out the cork with his fingertips in one move; this extremely valuable bottle of wine is visibly sealed (in every shot) with a thick, air-tight red wax. This wax must first be cut and peeled away to access the deeply-embedded cork, and the cork must then be removed with a wine key (corkscrew). The action of properly opening the bottle would have required more time than the entire scene itself; so, to expedite the flow of the shot, director Terry Gilliam deliberately chose to forego a proper uncorking.
Continuity mistake: When Munchausen is about to be executed for the second time, right after the Sultain sais: "Executioner, execute!" we see the executioner raising the axe. The axe is facing the wrong way. In the next shot it's the right way. (01:39:45)