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.
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.