Continuity mistake: When the human chess game ends and Holmes hears Lestrade knocking from the secret passage, the distance between the detective and Captain MacIntosh changes between shots.
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.