received ticket for improper disposal of futon

Did they actually take the futon away? If so, pay; part of that $100 is fair compensation for their services. If they left the futon without taking it, they they're charging $100 for... what, exactly?

The Sanitation site says mattresses need to be sealed in plastic to help prevent spread of bedbugs.

The fine has been charged to the landlord and is part of his overhead. You could add it to next month's rent, and the bookkeeper might mention it to whoever writes the "wiivile was a good tenant" letter.

Bedbugs don't spread diseases to human beings. Bedbugs are adorable. Pay the fine.

Vote the Anybody But Quinnberg ticket.

how many lies from you?

I'm kind of confounded by this question. It seems pretty black and white to me. You should call the landlord, apologize for the ticket, explain that you weren't aware of the rules about how to dispose of mattresses and reimburse them for the ticket. Unless the super was somehow responsible for wrapping it up, there is really no grey area here.