As Blackthorn wakes up and discovers the tray of food, a pair of disposable chopsticks are clearly visible. Disposable chopsticks were invented around 1878 and didn't exist in the setting for the story. Besides, a family home would've had better kinds of chopsticks, most likely lacquered, and not disposable ones as they are used at restaurants where they have to be broken apart to prove that they aren't already used.
In the opening scene, a tracking aerial shot of the 16th century ship, you can clearly see the reflection of a helicopter in the sea.
When Blackthorn wake up in empty room after storm, in the moment he grab his hair, there is brief moving shadow on right side of screen, apparently from filming crew.
When Blackthorn (Richard Chamberlain) first wakes up following the shipwreck off the coast of Japan, he is in a Japanese house, separated from the rest of the ship's crew that washed ashore. But there is no reason for the Japanese villagers to have housed him separately. They have no knowledge of who he is, and there is nothing noteworthy such as uniform, rank insignia or other visible signs to distinguish him from the others.