Most remodel and cleanout debris is fine to load. The limits come from California's disposal rules and from what the receiving facility will take.
CalRecycle keeps a list of waste banned from the trash statewide. It includes every kind of battery, fluorescent tubes and other mercury lamps, paint of any type, solvents, motor oil, antifreeze, and propane tanks. TVs, monitors, laptops, printers, microwaves, and cell phones are on it too, since electronics often contain hazardous parts.
Two building items on that list catch remodelers off guard. Treated wood with chemical preservatives has to be handled as hazardous waste, and asbestos can turn up in older roofing, flooring, siding, and cement products. Tires are also banned from the trash.
California's Mattress Stewardship Program sends old mattresses, box springs, and futons to recycling instead of the landfill. Hazardous waste, liquids, and fuel can't go in a standard dumpster either.
If an item on your list gives you pause, check with your account manager before it goes in.