The credits call Edmund's mother "Gertrude, Queen of Flanders". However, Flanders never had a queen, since it was never a kingdom. There was a medieval and early-modern county of Flanders, existing from 862 up until 1795.
Calling Richard IV of England "Richard XII of Scotland" is a joke about the fact that James I of England was James VI of Scotland. However Scotland never had any kings called Richard, let alone 11 of them.
England and Scotland were two separate kingdoms in 1485. There was no personal union between them until 1603, when king James VI of Scotland also inherited the English throne as James I.
When the cannon explodes at the end, and Prince Harry thinks it is the drains, he says he will get his plunger, but these were not invented until 1874 in New York City.
Edmund refers to some letters as "slanderous." He should have said libellous, as slander is verbal.
In the hunting scene McAngus tries but fails to sheath his dagger after using it to skin an animal, but instead holds it in place until his back is turned. With The Black Adder hanging upside-down behind him a reshoot was presumably not thought desirable.