Can I sue a company for selling me a dirty used mattress?

You can sue anybody you want to, but whether you win or not is a different thing all together. If this is a corporation, make sure you sue them in their proper name, or else the case will get thrown out of court. There are too many details involved to give you a simple answer. Whether or not you have a chance to win if you sue depends on what was represented about the furniture at the time of the sale. It sounds like "staged" = floor samples, which are typically used furniture, so there is no way the mattress and box spring were "new". Did you inspect the mattress and box spring before purchase? Were they wrapped in plastic? Did you sign anything? If so, what does that say?