Hans Holbein the Younger died in 1543 at the age of 45, so he could not have painted Henry VIII in 1547. Holbein's most famous surviving portrait of Henry VIII was painted in 1537.
Charles Brandon, 1st Duke of Suffolk died in 1544, not in 1547 as depicted here.
In this episode and throughout the series Henry and others give his title as 'King of England, Ireland, and France'. The correct form in use at the time was 'King of England, France, and Ireland' as France, albeit held in pretense, was the more important title.
Holbein looks the same as he did the first time he was on screen even though though the king and Charles Brandon have aged significantly and there is slightly more than a decade between when he is first shown and the King dies.
Even if Holbein had been alive at the time Henry says that Holbein painted his father at the end. The man playing Holbein looks like he was about 40. Henry VII died in 1509 and Henry VIII died in 1547 so that would have been impossible.