David Riccio is calling the Scottish currency "Crown". The correct term would be "Sterling".
In the movie Henry Darnley led Riccio being killed long after the birth of their son James. However in real life Riccio was killed while Mary was pregnant.
David Rizzio said that he is from Bologna. However he was originally from Pancalieri, Italy, which is far away from Bologna. Also he came to Scotland from Savoy, France.
The court is showing letters written by Mary to prove her guilt. However in the later centuries it was said that these letters are fake as the actual letters were destroyed in 1584 and the copies didn't recreate the original content. Also it is not proven if the letters actually show her guilt on the murder if her husband Lord Henry Darnley.
The movie suggests that Mary married Lord Darnley only to have a Scot as a regent on the throne. However according to sources she was in love with him.
In the first scene of the movie Maria Stuart is playing Domino. This type of dominoes which were shown in the movie (with square halves) wasn't spread in Europe until the 18th century and it was first in Italy. While there are reports that Marco Polo brought them to Europe from China in the 13th-14th century and the word "domino" was known in the 1000s, the game itself looked completely different than in the movie.
Mary announced as a possible husband the Russian Czar, the Spanish infante, the king of Sweden and the German emperor. However the actual regents who asked to marry Mary were, beside the king of Sweden and King Don Carlos of Spain, also the king of Denmark, France, the arch duke Karl of Austria, the princes of Ferrana, Namur and Anjou as well as the Earl of Arran and the Earl of Leicester.