Niccolò Machiavelli was a journalist and historian, not an arms dealer and assassin as depicted here. The writers may have confused Machiavelli with Prince Cesare Borgia, the subject of Machiavelli's famous report.
The Confederates in the same unit wear both cavalry and infantry uniforms, but it's a cavalry unit. The Confederate artillerymen also wear cavalry uniforms.
The Union "Major" wears the silver oak leaves rank of a Lieutenant-Colonel.
When Doug and the Major reach the other side of the stream, the Major takes off his boots and pours water out of them. He is soaked from being in the water. However, Doug seems completely dry, even though he was supposed to have followed the Major across the stream.
In the opening scene, one of the soldiers begins to fall to the ground before the bomb blows up behind him.
Though set in summer, some scenes show the trees are bare and the ground is covered with dead leaves, indicating it is late autumn. Other scenes correctly show the trees full of green leaves.
When Doug & Tony are in the cave, unconscious, before transfer, their Civil War uniforms are not dematerialized and switched for their usual attire, as is normally done. But when they are being transferred one sees their attire changed after the fact. This same instance first took place in Invasion (1966).
When Doug and the Major are about to cross the stream, they move all the way to the right and move off camera, apparently before abruptly making a 180° turn to enter the stream. This was done to allow the actors to move out of the way so that their stunt doubles could pass as them before entering the stream.
When Tony and the Major split up and cross the stream, one can see a modern highway bridge in the background.
At about the 46 minute mark, when Doug and Tony are struggling on the suspension bridge there are electrical power lines visible in the background.
The Union jackets and weapons are from the Indian Wars period of the 1870s-1880s, not 1860s Civil War items.
The artillery is fired using burning linstocks to ignite priming powder, but this was obsolete by the time of the Civil War, when field artillery cannons were fired by pulling a lanyard attached to a friction primer.
When Machiavelli is fleeing from Doug and Tony, he is heard laughing, but his mouth isn't moving.
There was no Wilson's Creek and no suspension bridge near Gettysburg. There was a Battle of Wilson's Creek, but it took place in southwestern Missouri about two years before this.