Most renovation and cleanout debris is fine for your container. New York State rules and local facilities set the limits.
The New York State Department of Environmental Conservation bans electronics from the trash, and that ban has been in place since January 1, 2015. Computers, tablets, monitors, printers, game consoles, and most TVs can't go to a landfill, a waste-to-energy plant, or the curb. State law also prohibits burying waste tires in landfills.
Hazardous waste, liquids, paint, solvents, fuel, propane tanks, and asbestos can't go in a standard dumpster either. For household chemicals, the Village's refuse page points residents to the Town of North Hempstead at 516-869-6311.
Mineola's Sanitation Division picks up appliances and metal items by appointment, up to two items at a time, if you call 516-746-6791. That's an easy way to keep them out of your dumpster.
If an item seems borderline, check with your account manager first.