In season three Henry VIII mentions Catherine of Aragon's nephew and calls him Charles V of Spain. This is not correct. He was Holy Roman Emperor Charles V, but in Spain he was King Charles I.
Pontefract Castle is shown throughout the series as placed between two large, steep hills when in fact it was on a high point of ground much higher than anything within miles. (During the civil war a nearby hill was built up to place cannon to attack the castle but in Tudor times it didn't exist!)
The tun Henry and Jane dance to, "The Twenty-ninth of May," was written to celebrate Oak Apple Day, which commemorates when Charles II returned to England in 1660, from exile in France, 124 years after the wedding day of Jane Seymour and Henry VIII.