The slimy stuff could be a piece of the old tube. I'm not sure if dusters get any diseases or not, I've never heard of that happening but I'm sure they can harbor parasites of some sort. I had one lose its feathers and it did grow them back in a week or so. If the duster is down on the sand, be sure you don't have any scavenger critters like hermits or small crabs that might go after it. Otherwise I'd leave it alone, keep the water quality up and see what happens.
If you do get another one, don't get one that doesn't have an intact tube. The duster should also be able to completely pull back into its tube if disturbed, and should do so quickly (check this before you buy any duster).