If I have a comedy club and a comedian becomes obscene, am I responsible if legal action is taken?

Probably not, but it depends on what type of legal action, the exact language of the waiver and your state's laws.

YOu need to define obscene. Facts and question as stated is vague. Is it something comedian says (words) or does (action)? It also depends on what happened and how serious is it. What kind of legal action are we talking about? Please provide more facts.