In this movie, set in 1910, Sir Arthur Conan Doyle has "only" gray hair. In real life he was a brunette and had a mustache.
Although the dialog says that "Holmes" is wearing an Inverness cloak and a deerstalker hat, and has a Meerschaum pipe in his mouth, in fact, he does not.
He is wearing a coat with crisscross stripes, sports a large round check cloth cap, and has a small straight pipe in his mouth.