In my opinion the reason Mrs. Watson showed the class an episode of the Cosby Show was to teach the class a lesson.
Older sitcoms usually include a lesson the producers incorporated with the show. In this episode the producers taught the viewers that it is necessary to make sure a person is prepared to do something before they follow through with the action. They also showed presentation is very important.
Ms. Watson was trying to teach the class to be prepared by playing an episode of the Cosby Show.
