I was thinking of using some nylon stockings as a hop-bag for dry hopping in my fermentor. Are they safe to use or will they be degraded by the wort?
They are completely safe to use. I personally steer clear of colored nylon stockings. If you're worried about bacteria you can soak them in a bleach mixture overnight, rise out, and then boil them. You could also soak them in Star San after boiling (if you're a germaphobe like me!).
Make sure you tie them and ensure there aren't any holes. Also, if you're using a lot of hops you can use multiple nylon stockings so your hops aren't as bunched up. I also use a light stainless steal "mixer" from a protein bottle to keep them from floating at the surface.