Deliberate mistake: After the black ninja and white ninja clash swords for the first time, the black ninja pretends to put his sword in its sheath, which is slung over his back, rather than actually doing it.
Factual error: The training set piece is supposedly Japan, but it's obviously taking place in the Philippines. Its biggest giveaway is the presence of Taal Volcano.
Visible crew/equipment: During the opening sequence Cole does a backflip to get down from a tree and lands behind some tall grass, as he pushes the grass aside and steps through you can see the stuntman who did the backflip trying to hide behind him.
