One subject could be the duplicity of identity in the character roles. There is more than one person either pretending to be or mistaken as being someone else, including Holmes.
Another subject you could develop is that of poetic justice. In this story, at least, the "bad guy" gets just what he deserves.
Or, with your teacher's permission, you could delve into the processes of inductive and deductive reasoning, both present in this mystery intrigue.
Another possibility would be Doyle's motivation in writing the story in the first place. For more information concerning this, see the eNotes reference below.