Factual error: When they first meet, Rodrigues tells Blackthorne that aboard his ship there is plenty of food and grog. The problem is that grog was not "invented" until 1740, when it was introduced into the British Navy by Admiral Edward Vernon, who was nicknamed "Old Grog" because of his habit of wearing a grogram coat.
Factual error: When Rodriguez is in his cabin with Blackthorne after having been saved by Yabu, he tells Blackthorne, "There's a bottle of grog over there." Grog was only invented, as it were, in 1740 by British Vice Admiral Edward Vernon, whose nickname was "Old Grog" because he wore a cloak of grogram cloth.
Factual error: Throughout the show, flintlock firearms are used. The show is set in 1600, and the flintlock was not invented until about 1630.