Juana refers to Anthony as "Duke of Wellington". This is in 1810. Sir Arthur Wellesley was elevated to the Peerage after the Battle of Talavera and to a Dukedom in 1814. In 1810 he was still Sir Arthur. The post of Duke of Wellington did not exist.
When the cannon breaks loose and races down a hill it hits a ditch and bounces out coming to rest on the other side. In the next shot, the captain is inspecting the damage as the cannon rests squarely in the middle of the ditch that we've just seen it bounce out of.
When the cannon is being floated over a river on a raft, one of the four drag lines breaks, allowing the gun to charge down the river through rapids, eventually crashing on a rock. When the raft is shooting the rapids, however, all four lines are trailed out on either side, including the "broken" one.
When Anthony (Cary Grant) and Miguel (Frank Sinatra) jump off the cannon as it's rolling down the hill, their stunt doubles jump onto ground and it rebounds up into the air all around them and shows to be a net. Clearly there is a spring-loaded catch net in the ground to soften their fall. And they don't roll or tumble, just hit the ground and bounce and stop, even though the cannon is rolling pretty fast.
When the peasants attack the military camp in the mountains, a peasant throws a firebrand onto a tent which rapidly catches fire. But as he is throwing the firebrand, the tent is clearly visible with a pattern of liquid that was splashed or poured onto it from the top down, and that part of the tent that was wet is the part that rapidly catches fire, showing it to be an inflammatory agent such as fuel oil or kerosene.
On the wall of the French army general staff there is a map of the region of "Las Cruces" (actually Galicia, northwest Spain). The river passing through Orense city is marked like Rio Duero. In fact it is Miño river which passes through Orense and delineates a section of the border between Spain and Portugal. The Duero river is further south, crosses the Castilian plateau and has its mouth at the Portuguese city of Porto. In the film it is named Rio Cano.
The French commander at Avila, after sentencing 10 peasants to death, supposedly signed multiple documents with the same quill pen without dipping it into the inkwell frequently as must be done with quill pens.
After the wall has been breached the commander of the French Garrison orders the Captain to "Mass your rifles in the square". The French army did not use rifles in the Peninsular war as Napoleon had discarded them as being too slow to reload.
The French commander at Avila threatened local peasants to tell him where the cannon was shortly after the journey to Avila with the cannon started, but Avila was far away from the cannon and the cannon was heading toward Avila and the peasants couldn't have even known where it was or even known about it. Word did not travel that fast in those days.
During the attack on the military camp in the mountains, the flaming balls of dried grass roll down the mountainside into two different gunpowder caches which explode instantaneously. The fireballs would at least have to burn for a time to burn up the containers storing the gunpowder before it could explode. And no military stored it carelessly so that the slightest spark would set it off, it's too valuable for their efforts and is handled and stored with extreme caution.
After the cannon has tumbled down the hillside it comes to rest in a ditch. The Englishman inspects it and proclaims that the barrel has been separated from the carriage. But in plain view the cannon has almost broken in two since it is not of metal.
During the knife fight scene with Carlos, Anthony (Cary Grant) holds his knife backwards, with the sharp edge facing himself instead of toward Carlos. Carlos holds his correctly, with the sharp edge facing Anthony.
When the cannon hits the ditch at the end of the roll and breaks, the pivot part of the barrel that breaks off is clearly wooden. A large chunk of it breaks off of the cannon barrel and looks like a tree trunk does when it is split, with large wood fibers clearly visible. This shows that the cannon is made of wood and not metal.
When firing the big gun at the castle, for the first few shots there was an appropriate delay of a couple seconds between the cannon firing and the impact blowing out chunks of the castle wall. But right when the peasants are signaled to charge the castle, the cannon is fired and nothing happens for 3-4 seconds and then the explosion happens, clearly a faulty delay in the charge placed in the wall to simulate a cannonball impact.