Audio problem: When Holmes and Watson are about to go out to the Blackhorse Tavern the second time, Holmes answers Watson's question as to where they're going by saying "the Blackhorse Tavern." However, his lips do not move.
Continuity mistake: When Watson is conned by the prostitute who says she knows Mary Kelly, she lures him into a closed alley. After Watson has called the police and subdued the attacker, 2 constables arrive and arrest Watson, but as they all leave, a third constable comes from behind the camera. Either he magically appeared, or he walked through the wall behind.