Major Plot hole: Lord Blackwood fakes his hanging execution at the beginning of the movie. So obviously, Dr. Watson who is in charge of confirming his death will take his pulse instead of checking if the rope really broke his neck.
He did check the pulse, but Blackwood hat taken a tonic that decreased his heartbeat to near undetectable. So this "plothole" is untrue.
I think you are misunderstanding the phrasing of the original article. Execution by hanging is supposed to break the victim's neck, so death is instantaneous instead of slow and drawn out. The plot hole is that Dr. Watson (who is supposed to be very smart), only checks Lord Blackwood's pulse and doesn't check if Blackwood's neck is broken.
If he had checked Blackwood's neck, Watson would have realized that his neck wasn't broken and also that he hadn't been strangled, which would mean the hanging didn't kill him. This would have been extremely suspicious and would probably have been enough for the police to delay his burial (since he was such a high profile murderer), which would mean that Blackwood would have gotten caught as soon as his tonic wore off.
The Anatomy Act of 1832 directed that the bodies of all executed criminals belonged to the Crown and were buried in the prison grounds in unmarked graves. The body would not have left the prison - which, let's face it, is a big plot hole in itself. But the main point is - we're dealing with a long drop hanging here! Lord Blackwood would have been a few inches taller and the marking to the face and neck would have been severe. There would have been an inquest. Only a non-medic (like you?) would ignore the injuries (or lack of them) and certify death just by feeling his pulse. This is a major plot hole and infuriating to anyone who takes even a passing interest in how these things worked.