Wouldn't have paid the Black Mail

One thing about this movie I never understood (one thing?) was why certain characters would pay the blackmail in the first place? Some like Peacock, Mustard, and Green would definitely have paid it for fear of losing their jobs or being thrown in jail. But the others:

Prof Plumb: Either his job at the UN didn't require him to have his medical license, or you would have to believe that the UN would have done basic background checks, and discovered that his license had been revoked. Either he didn't need it, or they already knew he didn't have one. And like he joked with Scarlet "You don't know how things work at the UN. I might go up in some estimations." No need to pay a blackmailer.

Mrs. White: She would have to have been the first person the police investigated, especially since she has had previous husbands disappear, and her and her husband had a very public fight. Obviously she was cleared by police and no longer a suspect. Just because Yvette admitted to sleeping with him, would not be enough evidence to arrest her, so unless Mr. Boddy had some other peace of crucial evidence, then she wouldn't have to pay.

Mrs. Scarlet: She runs a high end escort service in the DC area. Just like Mr. Green says "Half of Washington knows what kind of business you run. The whole town would be implicated if you were exposed." She had to have more than 1 cop on her payroll. Even if the one came in and threatened her, she could have the others help her out, or some of her political clients could make the charges go away. She would have laughed in the cops and Mr. Boddy's face when they tried to threaten her.