Deliberate mistake: The window blind in Maroon's office changes to a sheet of tambour (as found in roll-top desks) just before Roger crashes through it. This was to ensure his outline remains perfectly in it, otherwise pieces would drop out which are not attached to the strings on either side. (00:23:25)
Deliberate mistake: When the boy jumps on the Police motor tricycle and his father jumps on as pillion passenger it is obvious in the subsequent scenes that a small but adult stand-in is riding the trike.
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.
Suggested correction: You're ignoring the fact that the entire scene is a story the real Munchausen is telling from memory. There are many fantastic elements that do not hold with reality, like him riding his horse out of the window, falling several stories, and landing safety, or Adolphus being able to see and shoot to the other side of the world. The bottle is simply an example of Munchausen not adhering to reality.
In any event, the Sultan's effortless uncorking of the bottle was a deliberate mistake intended to allow a whole series of actions to occur sequentially in the single wide shot in less than 5 seconds.
Yet, at the end, Sally addresses Baron Munchausen directly and asks him the question that the audience has been wondering throughout the whole movie: "It wasn't just a story, was it?" The Baron solemnly shakes his head, affirming that he was telling the truth all along, regardless of how fantastic it sounded. This point is often missed by the movie's critics.
The point I raised wasn't that the Baron's story wasn't true, but rather that he embellished it.
Deliberate mistake: In the end scene at the TV set, Scrooge tosses a coin out the window, and the camera follows the coin as it falls in slow motion. The people in the control room also watch this on their monitors. Problem is, this is a live broadcast and filming/watching something live in slow motion is impossible.