At the beginning, the scientists are watching through the tunnel the guillotine blade is being drawn up by a rope. When the close-up of it being dropped is shown there is no rope attached to it.
While breaking the Dauphin out of prison, Tony and Doug each fire their rifles twice, with not more than a second between shots. But they are muzzle loaders that couldn't have been fired a second time without reloading.
According to this episode, Marie Antoinette was executed on October 15th 1793. In fact, it occurred on October 16th.
In the closing credits, Joe E. Tata is listed as playing "Napoleon Bonapart." The correct spelling is Napoléon Bonaparte.
After they help the Dauphin to escape, there is a fight in the street outside the prison. At the end of the fight, one of the guards barely kicks what appears to be a solid, metal lamp post, and it sways back and forth several inches.
During the fight scene after Doug and Tony help the Dauphin escape, one of the guards is shown lunging at Tony and actually grabbing hold of him, but in another shot, the guard knocks into both Tony and Doug.