When Leslie is putting on the parachute in the hot air balloon, there's a shot of the crowd below in which the spectators are clearly visible, not much more than a hundred feet below. But when he jumps, the pull back shot is much higher, possibly thousands of feet.
The balloon was supposed to be losing altitude due to the hole from Professor Fate's arrow. Additionally, the first shot is likely not high enough for a parachute to work.
When Professor Fate is fleeing from the "Indians" he turns on the smoke screen. In long shots the smoke can clearly be seen filling the car's interior. In close-up the car is smoke free.
During Lily Olay's musical number, the amount of foam in Professor Fate's beer changes radically when she blows it in his face.
When the Leslie Special car is being pushed out of the garage its on red carpet immediately in front of the garage. When viewed from above the red carpet is now just surrounding the car. There's no red carpet in front of the garage's opening.
At the and of the pie-throwing scene (done on an interior set), Natalie Wood is thoroughly covered with pie filling, topping, and crust. When she is seen entering the car (an exterior shot), though this ostensibly takes place just moments after the end of the pie fight, she is now only picturesquely dabbed with pie debris.
Maggie Dubois sends photo negatives to the newspaper by using homing pigeons. The negatives from the camera she is using would be too heavy for a pigeon to carry. Also, since there is no protective covering, the negative would have been ruined long before reaching its destination.
Dr Fate's submarine would not operate under water using a paddle wheel as shown. The submarine would stay in one place.
When Leslie reaches the Eiffel Tower, there's a banner with the word "FINIS" on it. In correct French, one should have been "ARRIVEE". "Finis" is more or less an accurate translation of "ended" or "Finish".
The french counterparts for START/FINISH are indeed DEPART/ARRIVEE.
Leslie's comment about being warmed by alcohol is in error; an error that is often presented in film and on TV. This can be very dangerous if viewers were to try this. As alcohol is a depressant, it lowers the body temperature, which seems to make one feel warmer. In actual freezing conditions, drinking alcohol would increase one's risk of hypothermia and death.
The sabers Baron von Stuppe and Leslie fight with have the sort of blades used in sport competitions. Sabers used in actual combat have much wider and heavier blades.
In the final sprint to Paris, Maggie DuBois's costume changes. Since her costume changes at a phenomenal rate throughout the film, this was probably intentional.
When Leslie drives on the beach his tires are heard to screech when he brakes. Tires will only screech on pavement, never on sand or dirt. This was possibly intentional, as the film is a spoof. But movie sound technicians often get this wrong as tires don't screech on sand or other soft surfaces.
A left-handed musician playing a guitar (or similar instrument) up side down without restringing it is not an error. Many left-handed musicians do this.
Leslie agrees to take Maggie Dubois to Grommet if she sends a homing pigeon ahead of them with a message to send for gasoline. But since homing pigeons are bred to return to the place they nested from, it would be impossible to get one of hers to fly to Grommet. However, the pigeon isn't supposed to fly to Grommet at all; the idea is that it flies back to the newspaper office and a telegram can be sent from there.
Professor Fate's car, the Hannibal Twin 8, has the ability to elevate the chassis above the ground. However, whenever this function is used, both the engine and drive train of the vehicle also rise, leaving the wheels on the ground with no method of propulsion nor steering. So the car is driving around on wheels apparently not powered by anything. Note that while the car is being driven around the castle courtyard, small boxes are visible next to the rear wheels: these are almost certainly batteries for an electric motor. And in this example, with there being no ability to steer, the wheels were almost certainly fixed to drive in a circle.
The guide wire is visible on the missile following Professor Fate's car.
When Frisbee loses his footing when retrieving the pigeon at the newspaper office, his right leg "disappears" as he hangs from the ledge. This is due to his leg swinging into the matte shot that was created to "place" him into the shot to complete the building's appearance - the initial setup was done on a soundstage.
During the hot air balloon scene, wires on the balloon are clearly seen.
When Fate first reveals the Hannibal Twin 8 to Max, the camera pulls back to a wide shot. To change from the dramatic lighting of the close up, you can see many more off-camera lights being switched on to light up the entire garage for the reveal of the car.
The large American flag hanging outside a window (with the French flag) near the beginning of the race has 48 stars. In 1908, when this movie supposedly takes place, there were only 46 states (New Mexico and Arizona were admitted in 1912, and Alaska and Hawaii were admitted in 1959). Many flags (perhaps all, it's hard to tell) being waved by the crowd have 46 stars.
Set in 1908, TV antennae visible on the Eiffel Tower.
When Professor Fate is lifted by an airplane flown by Max, the plane resembles a Curtiss Headless Pusher. This plane was not designed and built until 1912, four years after the year in which this movie was set. In July of 1908 Glenn Curtiss flew his June Bug design, which was the first public exhibition of flight in the US (the Wright Brothers had not yet flown publicly). The 1908 June Bug and the 1912 Headless Pusher bear little resemblance to each other. In reality, the June Bug was not as nimble and stable as the Pusher, so it is understandable why the 1912 design was used in the movie.
The Great Leslie exits the balloon using a knapsack parachute. This was not invented until 1911 three years after the year in which the movie is set.
In the scene on the beach in the tent when Leslie and Maggie DuBois drink champagne, Leslie puts on a phonograph record of "The Desert Song." The film is set in about 1908; "The Desert Song" did not premiere until 1926.
In the saloon scenes several gunshots have no accompanying sound effect.
During the pie fight (particularly at the start), the sound of a 35mm still camera's motor drive can be heard.
As the Baron prepares to jump out the window after the sword-fight with Leslie, he attributes his parting quip to "a famous English gentleman" that starts out "He who fights and runs away . . . ". That passage, however, is from a poem by Oliver Goldsmith, a doctor from Ireland.
Baron Von Stuppe is known, according to Prince Hoepnick, for his swordsmanship. It is odd that he would not be aware that Leslie had won the "International Men's Fencing Championship" when he asks Leslie if he know how to use a foil.