Legal Question in Landlord & Tenant Law in Washington

This is a close one. I think it would depend on whether the management knew or should have known they had a mold issue before you moved in. If they new or should have known, then I'd say they were negligent in letting you move in without warning you, and on that basis, a court could find them liable for paying you the fair market value of your then used mattress, not a new or replacement cost.

You'll probably be in small claims without an attorney to help you, unless you have a particularly pricey mattress. You probably do not have much to lose, but read over your lease very carefully before suing your landlord, because there may be a clause in there that says that if you guys wind up in court, the prevailing party gets their attorney fees paid by the losing party. If your landlord is a corporation, even in small claims they are going to have an attorney represent the corporation. The law requires this. If that's the case, and you lose, you may be liable for that attorney's time spent defending against you.

Ask yourself what the value of your used mattress would be, say on Craigslist, if you were to try and buy a used replacement that is free of mold, then consider if that cost makes it worth suing over and spending the time chasing after that issue. It seems to me that your landlord tried to do right by you, when they let you move into another unit, as they should have, so I am not looking at them as slumlords at this point. Bear this in mind when you sue them and inevitably make an enemy out of them.