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.
Revealing mistake: As Holmes and Watson are riding home from Watson's stay in prison, in the background double traffic lines are visible as are concrete traffic barriers. These are a modern invention and out of place.
Revealing mistake: At the end, when the inspector is stabbed by one of the murderers, he falls back into a sturdy looking fence that breaks apart. As he is lying there, you can see the pre-cuts on the wood so that the fence would break cleanly in a specific spot.
Factual error: When Holmes gets rundown by the carriage, he gets taken home and Watson ministers to his head wound. Holmes gets up a short time later and refers to the carriage as a hansom, which is a little two-wheeled cab. The attacker drove a brougham, with four wheels and four-in-hand horses. Even with a slightly bruised head, the master of observation would never make this simple yet telling mistake as he's shown seeing the carriage. The type of carriage is vital to the plot later as it suggests the wealth and status of the murderer and it appears to be used to commit the crimes.
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.