At around 17:10min mark, when Mary approaches Francis's door, the actress first approaches with her right had raised to knock on the door, then in next cut she's knocking with her left hand.
Diane de Poitiers, maitresse of King Henry II, had only two daughters with her deceased husband, no son ("Sebastian") with the King who was 20 years younger than her.
After the first assassination attempt, the abbess states that it was the work of the "Protestant throne of England". However, in 1557 Mary I, a staunch Roman Catholic, ruled England and would do so until the following year.
In real life after the marriage of Phillip II and Elisabeth there was a joust in honor of them where King Henry was killed. In the show he is alive and well for some time afterward.
It looks like there's a zipper on the back of one of the dresses. Zippers weren't invented until much later.
The newly arrived Mary of Stuart, Queen of Scots attends the wedding of Elisabeth of Valois to Phillip II of Spain, but in the following episode Mary clearly says to the English war soldier that she heard that Queen Mary I of England is sick and maybe her sister Elizabeth (whom we now know as Elizabeth I of England) may soon take the throne. Phillip II of Spain was married to Mary I of England and could never have married Elisabeth of Valois at that moment. The wedding between Elisabeth of Valois and Phillip II indeed took place (in 1559), but not until the death of Mary I of England in 1558 and a failed wedding proposal to Elizabeth I. It was in the same year that Mary of Stuart married to Francis.
When Mary's dog runs away Bash tells her that the dog would rather be in the warmth of the castle than the cold woods. It happens right before the wedding of Elisabeth de Valois and Phillip II of Spain which was in June of 1559 so it would not have been cold.
The French court isn't nor ever was located at the sea. Paris is 120 miles away from the coast.