Most debris from a remodel or cleanout can go in your container. California's trash bans and the transfer station's rules set the limits.
California's recycling agency, CalRecycle, bans electronics from the trash. TVs, monitors, laptops, computer towers, printers, microwaves, and cell phones all need to be recycled instead. Batteries of every kind are banned too, from small household cells to car batteries, along with fluorescent lamps and LED bulbs.
Other items on the state's list include paint, solvents, motor oil and filters, antifreeze, pesticides, propane tanks, tires, and chemically treated wood. Asbestos from older siding, roofing, or flooring needs special handling.
Hazardous waste, liquids, and fuel can't go in a standard dumpster either. Pull those out before you start loading, and mention mattresses, appliances, and tires when you book, since Shoreway charges for some of them by the piece.
When in doubt, check with your account manager before loading an item.