The professor's beatings of the unarmed men are criminal assault, and would result in his prosecution and disbarment, not in approval.
The good guys plant a movie camera in the wall of the villain's apartment to spy on them. We see the lens barely peeping from the wall behind a china figurine. Yet, when they show the film later as evidence, the camera tilts, pans, and frames all the action from various angles, which would not have been possible given the setup.
The professor says that you can tell hoodlums are cowards because they are always in groups, never alone. Yet the two murders that have already taken place were committed by lone assassins.