A few notes

I just saw most of the first episode.

Catherine of Aragon was born 16 December 1485, Arthur Prince of Wales was born 19/20 September 1486, and the future Henry VIII was born 28 June 1491. Thus they were aged 15 years, 10 months and 29 days, 15 years 1 month, and 25 days, and 10 years, 4 months, and 17 days respectively, when Catherine and Arthur were married on 14 November 1501.

Thus Catherine and Arthur are probably depicted as looking older and more mature than they actually did, while Henry is definitely depicted as being way too old in the first episode.

I note that a typical Tudor style country house was used for Dogmersfield House. Which makes sense because 1501 when Catherine came to England was during the Tudor dynasty that lasted from 1485 to 1603, right? Except that it took time for the new style to develop and sixteen years after the start of the Tudor dynasty seems a little early. And many landowners might take years or decades to rebuild their houses at great expense in the new style, so it seems a little odd that Dogmersfield House looks Tudor instead of medieval.

I believe that I head someone mention the "Habsburg empire" in 1501. That was an anachronistic expression. There was never a realm officially called "The Habsburg Empire", and loosely calling the Habsburg lands the "Habsburg Empire" was not yet a common practice.

In 1501 the only empire in western, Catholic, Latin Europe was the Holy Roman Empire, more or less considered to be the only empire. It is true that a member of the Habsburg dynasty was King of the Romans and future emperor, but the emperorship was elective and didn't belong to the Habsburg dynasty by hereditary right.

Furthermore, Spain was not ruled by the Habsburgs yet. Catharine's mother Isabella I, Queen Regnant of Castille, Leon, etc., etc., and Catherine's father Ferdinand II, King of Aragon, Valancia, etc., etc., were both still alive and ruling, dying in 1504 and 1516 respectively.

Catherine's Brother John, Prince of Asturias (1478-1497) had died without children, leaving Catharine's sister Isabella (1470-1498) as the heir to Castile, etc., and after her death without children the next sister Joanna la Loca (1479-1555) was the heir to the throne of Castile. And it was true that Joanna was married to a Habsburg, Philip the Handsome (1478-1506) Duke of Burgundy, etc., who did become King of Castile jure uxoris (by right of wife) in 1504. And they did have three Habsburg children including the future King of the Spains and Emperor Charles V (1500-1558).

But the future is always unknown and in 1501 it was always possible that a mere five deaths could have prevented the inheritance of Spain by the Habsburgs and made Catherine's sister Maria (1482-1517) Queen of the Spains, and a few more deaths would have eliminated Maria and her heirs and made Catharine herself the Queen of the Spanish kingdoms. Spain was not yet guaranteed to be ruled by the Habsburgs.