Eurus tells Sherlock that he has to solve his first case ever - 'The Musgrave Ritual'. In the works of Sir Arthur Conan Doyle "The Adventure of the Musgrave Ritual" is (chronologically) the first case solved by Holmes.
Stick figures are drawn on a chalkboard for a case Sherlock is solving. This is a nod to original Holmes story "The Adventure of the Dancing Men".
The final scene shows Holmes and Watson running from a building. On the pillars to their left and right are brass signs inscribed with "Rathbone Place". This is quite possibly a subtle homage to Basil Rathbone, an actor who played a version of Sherlock Holmes in the 1940's. Many think that Rathbone had the quintessential Holmesian look with his lanky build, long face, dark hair, and - most especially - aquiline nose.
Sherlock solves a case involving three Garrideb brothers. This is a reference to Doyle's story "The Adventure of the Three Garridebs".
Surviving notes show that 'Sherrinford' was one of the names Arthur Conan Doyle considered for Sherlock Holmes himself. Other writers have used the name for an older brother.