Plot hole: The opera house is directly above the Phantom's hideout in the sewers, with an orchestra booming loudly overhead almost every night (the Phantom plainly hears the orchestra), but this constant vibration doesn't affect the integrity of the subterranean structure. But at the end, the noise of two simple gunshots causes the Phantom's hideout and a massive part of the sewer system to collapse.
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.