Mustiness is the quality of being stale and damp. If your friend complains about the mustiness of your attic bedroom, you might want to open a window.
You can use the noun mustiness for things that are literally moldy or mildewed — the slight mustiness of old library books is actually kind of pleasant, while the mustiness of your neighbors' house makes you feel a little ill. Mustiness also a good word for stale, tired ideas: "The mustiness of the movie's themes makes it much less exciting than all the car chases and explosions might lead you to believe."