Revealing mistake: Right after Father Alvito hands Blackthorne the Portuguese-Japanese dictionary, the Jesuit priests leave Blackthorne and his entourage to continue their journey onto the port of Nimazu. You can see the orange-robed clerics walk along a track that was obviously used by wheeled vehicles. You can see grass growing in the middle of the dirt road and none in the grooves. But in an earlier scene Father Alvito stated that only the Emperor was allowed to drive in a wheeled cart which he only did it on rare occasions for ceremonial purposes and for short distances as this would otherwise damage the roads (as the grooves testify).
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.