What are the comparative notes on the following: Holmes' idiosyncrasies, Watson's relationship with Holmes, use of red herrings, and depiction of police?
What you're asking for can be applied to most of the stories. You can get access to them on numerous websited on the internet. Enotes has the basic information you need however.
Sherlock Holmes has the uncanny ability to notice the tiniest of details that most of us would never see. He has a broad knowledge of many topics, and this helps him to solve his crimes as well. It's a game to Holmes to try to figure out and solve crimes, one that lets him "escape from the commonplaces of existence." His logic and power of reasoning allow him to put two and two together when most of us are still trying to determine what they are. He observes details most of us overlook in fighting the evil criminals of his society.
Dr. Watson is a devoted follower of Holmes and a willing participant in his adventures. He doesn't always understand what Holmes is doing or even why, but he trusts him to solve the crime. Dr. Watson admires Holmes and realizes his life is more interesting because of their adventures together.
A red herring is a false clue to try and throw the police and Holmes off the track of solving a crime. Therefore, appearance and reality can be deceiving. In this particular story, the criminals don't appear to be criminal-like in their appearance or behavior. Holmes feels he must trust the evidence rather than outward appearances.
The police aren't always shown in a positive light, but are depicted as inept, especially compared to Holmes.