In several of the scenes, it is highly noticeable that the flags and banners and tents used throughout the movie are machine stitched with modern double needle stitching. Also that the loops used to attached to poles are stitched in the "X in a box" style not used till very recently in history. For a clear example see (time-stamp)21m0s when the Samurai challenger in the silver mask and suit emerges from the tent and look at the banner in the background. The mechanical sewing machine will not have been invented for at least another 50 years after this historic incident had happened. and the sewing machine still would not reach Japan for many more decades.
Mika is awoken by the witch and told that Kai has been killed. The witch sticks a knife into the floorboard beside Mika's head. It is shown from different angles, however, when the witch is leaving the room, the knife is lying on a pillow. In the next shot, the knife is once again stuck in the floorboard.
When Mika visits Kai in his hut (after battling the monster), she is shown walking through the rain with a parasol. When she leaves, she uses the hood of her cape to protect her head, and the parasol has disappeared. (The parasol is outside the door and she can be seen reaching down for it.)
The goof item below may give away important plot points.
During the ceremony where Shogun Tsunayoshi is proclaiming the 47 Ronin are again Samurai, the rope strap holding on his helmet changes position throughout the scene (both above and below his chin in consecutive shots).
Shortly after he is released from the Dutch Island, Kai and Oishi are talking. The scene is apparently taking place in overcast or gloomy conditions but one shot of Kai talking shows his face brightly lit and his jaw casting a shadow on his neck, showing that this shot was taken in sunny conditions.