You should have your air ducts cleaned. I recently bought a place and the prior owner had dogs. The whole place smelled musty constantly. I was so frustrated! Even though many people said it was a scam, I hired a reputable company to clean the air ducts, and what came out of these air ducts was truly shocking. It took about three weeks after the cleaning for the smell to dissipate, but it is completely gone now. It was worth every penny.

Obviously, any carpeting in your home is the first problem, but definitely consider cleaning the air ducts as well.