Seasonal cleaning is something that most families dread having to do, especially if they have been lax in their cleaning duties in years past. In some of the extreme cases, the need to rent a dumpster might arise. However, instead of just renting a dumpster, I would recommend collaborating with your neighbors, and coordinating your schedules so that you could collectively rent a dumpster to save a pretty good chunk of change.
By renting a dumpster, you avoid the complication that comes with having the neighborhood garbage man not take everything you put at the curb. The garbage man already works hard enough, it is not his job to make sure that all your old mattresses are properly hauled off. I imagine that if you expected him to do that, you should also expect him to not like you too much. It is in both his and your best interest to get a roll-off dumpster and maybe save him a couple weeks of picking up anything from your house, instead of piling a bunch of busted furniture at your curb and expecting him to take care of it.
Think about the stuff that your garbage man has the opportunity to go through. Everything you throw out, he has the chance to go through and learn. The garbage man probably knows more about your life than your closest friends, realistically. I just want everyone to be aware of that. I am not a garbage man, but it seems like every time the garbage gets collected, there is always something in there that no one needs to know about. The garbage man knows.