The storyline quickly departs from the events of the opening scenes, which encompass a 1922 short story by Sir Arthur Conan Doyle. In "The Problem of Thor Bridge," a woman dies after being shot on a bridge, and the clues point to one person as the murderer. Sherlock's investigation reveals that the dead woman had arranged her own suicide solely to frame someone for her "murder."
When taking the polygraph the suspect gives long form answers. Polygraphers instruct test subjects to answer questions with a simple yes or no. This is necessary to more clearly discern a specific reaction at the moment of the response. Giving a long answer muddies the water.
Sherlock, at one point, calls Detective Coventry "Detective Hip Flask". That's the name of a comic book character created by British writer Richard Starkings.