In establishing shots introducing scenes in the Vatican St Peter's Basilica is shown complete. The dome of St Peter's was not completed until 1590, over 50 years after the time the series is set and over 20 years after Michaelangelo (who also appears) died. It may be that the producers decided to show the complete basilica in these establishing shots to make it recognizable to the audience.
As the series is set between 1491 and 1547, the fiddler is a major anachronism for several reasons. His instrument appears to be a Stradivarius design, the basis for most modern violins. Antonio Stradivari was born in 1644. The violin was held against the chest or stomach, not under the chin, until the 18th century. Finally, violin bows looked like small archery bows until the 19th century, when Francois Tourte invented the reverse curve bow.
In the series, Thomas Wyatt has an on-again/off-again relationship with Queen Catherine's lady-in-waiting. In real life, Wyatt married Elizabeth Brooke, daughter of Thomas Brooke, 8th Baron Cobham, in 1520. However, there is historical evidence that the real Wyatt was infatuated with Anne Boleyn, as shown in the series.
At the time, noblewomen wore hoods to conceal their hair as a sign of modesty, and free hair was considered scandalous. Most women in this series are shown with free hair. As a deeply religious woman, Katharine would not have been seen with her hair visible. She always wore an English gable hood which concealed the entire scalp.