Deliberate mistake: At the beginning, the carolers are on the porch singing. The camera never pans, so this means that the carolers are facing away from the house (towards Gate) - seems rather odd. The only reasons for this would have been to make the clean camera move through the crowd and up the house.
Deliberate mistake: When Ed's looking at the drawings done by the sketch artist near the start, he's flipping over a book of them. Trouble is that they all end up facing the camera, meaning that Ed must have been looking at the blank side - we see the blank pages briefly as he flips them. (00:14:30)
Deliberate mistake: Smoke from a smoke machine smells very acrid, is standard temperature and would never be confused with hot steam from a shower. The man with the knife would have suspected something is wrong once he was in range to smell and feel the "steam". (00:26:35)
Deliberate mistake: While in the Japanese bath you see the fat samurai swim in the "pool" with an underwater camera. But when on the surface you can see the "pool" is no more than a man's length, in other words he could not have been swimming in there. (00:42:45)