You should be fined! Why would you or your neighbor who owns the mattress expect your neighbors to pay for hauling your trash? 

You should never throw a mattress in a dumpster. Likewise old carpeting, kitchen cabinets, etc. For mattresses try calling Goodwill, Amvets, etc. They will pick them up.

Generally speaking, since such items are not easily included in the annual budget, it is not uncommon for owners to be responsible for the disposal (and cost) of items that are not to be considered “normal and routine”. This might include construction debris, furniture, mattresses, appliances etc. 
 
Should the property manager have made it clear that this dumpster was for landscaping only? The answer is… yes, it would have been a good idea. However, since the dumpster was obviously something that was placed there for a “special purpose”. There is no reason to assume it was for disposing of mattresses, regardless of where the dumpster was located. 
 
I assume that the fine’s purpose was not so much to punish you, but rather so that the association did not incur an expense that is not common to all of the owners, hence the fine was more to cover the expense in removing the item. Since you had taken the correct and appropriate action by removing the mattress that you had inadvertently placed in the dumpster, there is no reason to fine you, and the case should now be considered closed.  
 
So as to improve community life at your association, I would suggest that you contact your property manager nicely and ask that he/she communicate to the owners the appropriate way to dispose of large items. The manager should be able to provide a schedule of fees for each type of large item as well as how, when, and where the item is to be placed for pick up. Under some scenarios, there may be no charge to the owner -provided that the item is placed in a certain location on a certain day etc.. Some communities include the pickup of bulk items in their budget, but limit this service to 2-3 specific times per year. Thus your friend would have had to hold the mattress in her house until the next “bulk day”.  
 
Hope this helps.

Richard Blenden's comment was spot on.  
 
However, most municipal laws prohibit dumping so it may have been possible for legal action to have been taken.

Agreed, Richard's comments are completely reasonable. Dumpsters are a magnet for people dumping things. There's a cost involved in extra items -- we have had to tell owners and renters constantly that the dumpster is for regular, everyday trash in trash bags. It's not for random pieces of furniture that they want to get rid of.  
 
If you removed the item when you were told, it shouldn't be an issue, just an honest mistake and no harm done.  
 
I will admit that it gets frustrating as a board member when you feel something is common sense and it's not followed -- sometimes we lose our perspective rather than being friendly =)

I can understand that you made an honest mistake by placing the mattress in the dumpster. However, since you removed it as soon as you recieved the violation letter that should be the end of it. A fine cannot be imposed if the violation is cured by the date specified in the violation letter. In AZ, state law prohibits an HOA from imposing a fine before the member has the opportunity to meet with the board.

Why is the property manager fining a homeowner? Shouldn't that be a decision that is made by the condo association board?

Our dumpsters are for trash only, the HOA gets charged extra for dumping construction materials, furniture or appliances. If anyone has furniture or appliances they want dumped, they have to contact the resident manager office for a special pick up, which the owner has to pay for. If they are doing remodeling, the contractor (or owner) has to haul that away.

Wow, 
Thanks for all the responses. 
There have been assumptions made here. Our trash is picked up from a receptacle off the garage of the condo. We don't take our trash to a dumpster. 
 
The association normally _does_ bring in a dumpster twice a year just so that we can throw mattresses and junk away.  
 
My assumption was that this dumpster was one of the two times a year that we get a junk dumpster. Had there been any signage at all on the dumpster stating who owned it or that it was for a specific purpose, I would not have put the mattress in there in the first place.