Most building and household debris can go in. California's disposal rules and the transfer station's limits decide the rest.
CalRecycle's list of items banned from the trash is longer than many people expect. It includes all batteries, fluorescent tubes, LED bulbs, and electronics such as TVs, monitors, laptops, and printers.
Tires are on the list, and so are propane tanks and other gas cylinders. Wood treated with chemical preservatives counts as hazardous waste, and so does asbestos, which turns up in some older roofing, flooring, and siding.
Hazardous waste, liquids, paint, solvents, and fuel don't belong in a standard dumpster either. Pull those items before loading, and mention mattresses and appliances when you book.
Your account manager can check any item you're unsure about before it goes in.