Is there a 'bad guy' in the story 'A Study in Emerald'?

The detective investigates the crime scene and sees that the Old One was killed very precisely by a man who knows anatomy well. This suggests a doctor. There is ash on the mantelpiece as if someone has put out a pipe on it. Footprints at the crime scene suggest two men, one of whom has a limp. There is a word written high up on the wall, which must have been written by a tall man. The word is 'Rache' which means 'revenge' in German. This suggests the killers are members of the resistance against the Old Ones. The detective tries to find a place that the murder victim went to more than once, and finds a theater company. They visit the play and meet an actor called Vernet who is a tall, pipe-smoking man. The detective thinks the limping doctor is his friend, and that the doctor actually carried out the murder. The detective is correct in all this, but is still foiled by the criminals in the end.