When the Duke of Buckingham is too afraid to let go of the chopping block, Anthony Knivert comes up to stretch out his arms for him. In the next shot of the Duke, he is still holding onto the block, and then just before the ax falls in the last shot of him, his arms are stretched out again.
In the scene where Buckingham is being arrested for treason the collar on his coat is up and down several times in the same shot.
While Bessie Blount was famously one of Henry VIII's mistresses and did give Henry an illegitimate son (Henry FitzRoy), historically, her son did not die as a small child. FitzRoy died at the age of 17 in 1536, a month after the execution of Anne Boleyn and roughly 10 years before the death of his father, Henry VIII. Blount was also not married until after the birth of Henry FitzRoy.
Several historical sources refer specifically Anne Boleyn's dark eyes, as they were rare in the English court during the 16th century. In the series, Anne Boleyn (Natalie Dormer) has light blue eyes.
Sir Thomas Moore offers Cardinal Thomas Wolsey his condolences on "the Orsini Cardinal" having been elected Pope. There were no Orsini Cardinals elected Pope during the reign of King Henry VIII (1509-1547). During the reign of King Henry VIII there were no Orsini Cardinals at all.
When complaining that Catherine's nephew has won the imperial election, Henry asserts that he will no longer just be Charles V of Spain, but will now be Holy Roman Emperor. Actually, the young man had been Charles I of Spain; "Charles V" was his imperial name.
When Norfolk takes his son to see the King Charles Brandon gives him a ring that had once belonged to his father who it is said had been executed for treason by Henry VII. However that is not true. Norfolk's father General Thomas Howard lived a long life and did not die until well into the reign of Henry VIII and as is shown in the Starz TV show The Spanish Princess was instrumental in the victory at Flodden in 1516.
Henry VIII is seen celebrating the birth of his son and fires a flintlock musket to do so. However, this type of musket was not invented until 1630, a century later.
In the scene when Anne Boleyn is talking to her father there is a hawk in the courtyard which he carries for a while. It is a Harris Hawk (Parabuteo unicinctus) which is an American breed, not known in England in the 16th century.
Henry mentions reading Machiavelli's "The Prince" but it wasn't published as "The Prince" until 1532, five years after his death. Written in 1513, Machiavelli referred to his treatise as "Of Principalities" and it did get circulated in manuscript form in the 1510s.
Norfolk takes his son to received by the King. His son is a pre-teen or teen. In real life his two sons were still very young at the time the episode depicts and the oldest Henry who is later seen was only about 5.
The Field of the Cloth of Gold was set in Flanders, a very flat part of Northern France and not a valley with high hills as shown on screen.