My employer has closed the women's restroom indefinite because of the filth. Can they do that?

yes they have the right to do that. I work in a factory and we have this problem with our mens bathrooms but they just make someone clean it up. Also in reply to Crazy Horse's post if the company was to put cameras in the restrooms they could be sued for invasion of privacy.. I know I wouldnt want someone watching me go to the bathroom.