Other mistake: Holmes appears disguised as a Sikh, complete with turban and beard. Although his face is black, his hands are without any make up and are white as snow.
Plot hole: When Holmes starts the human chess game, he says, 'Who had entered the lists, the king's pale knight.' This refers to moving the white knight of the king's side. However, the ritual does not mention to which square it should move. Still having three possible squares to move to (since the knight is on its initial square and the game has already started), Holmes knows and indicates that the knight (Dr. Sexton) must move to square F3.