I only watch the show occasionally so I definitely don't remember everything right now but here are the inaccuracies that I noticed.

Mary didn't grow up in exile (was it a convent or something?) but was in fact living at court since the age of 6 and was constantly pampered by her future family, especially the king. She married Francis at 15 and he died after spending less than two years on the throne. He was 17 at the time and was a always sickly and weak. His brother that exists in the show didn't exist in real life but his parents had a bunch of other kids. After Francis' death, she quickly returned to Scotland and married her cousin, which again didn't last long because the guy ended up getting murdered, but they did have a son together. Mary then ended up marrying the guy who was accused of killing her husband and had to abdicate as a result of an uprising. She then seeked protection from Queen Elizabeth I, even though she tried to claim her throne several times. After almost two decades in custody, Mary was found guilty of plotting to assassinate Elizabeth, and was then executed. So since the TV show still seems to be stuck in the "Francis is alive and Mary lives in France" chapter, it's not very accurate at all.

And then you have the fashion, the hairstyles, the makeup, the music and dancing, the accents, the creepy sister living in the tunnels, the sexy Nostradamus, etc. that just don't make any sense.

Also, Mary's 4 female attendants didn't have weird names like Lola, Kenna (lol?), Greer and Aylee but were in fact all called Mary. They were known as the Four Mary’s.