Baldrick is seen preparing, and the Prince is later seen eating, toast made from processed sliced bread which was invented in the 20th century.
The Prince refers to the story 'The Prince and the Pauper' which was written by Mark Twain in the 1880s, 60 years after the end of the Regency.
Blackadder recommends Trafalgar as the site of a sea battle for Lord Nelson. In fact Trafalgar had already happened in 1805, 6 years before the Regency started.
Several times Blackadder refers to the Duke of Wellington as "the Iron Duke". At the time, he hadn't been given that nickname.
Although King George III of Great Britain was also Elector (later king) of Hanover, he was more British than German. George probably spoke English without an accent since he was born in England and never visited Germany.
The Duke of Wellington intends to kill the Prince Regent for having sexual relations with the Duke's nieces, due to having declared he would do this to anyone who took sexual advantage of members of his family. Regardless of the Duke's vow, threatening to kill the son of his king is an act of treason for which the Duke would surely be executed, yet at no point does any character seem aware of this, not even the normally cunning Blackadder or the Prince Regent himself.