Most remodeling and cleanout debris can go in your container. California's rules and the regional landfill set the limits.
California bans many household items from the trash. CalRecycle's list includes all batteries, fluorescent lamps and tubes, latex and oil-based paint, pesticides, antifreeze, motor oil and filters, tires, asbestos, propane tanks, treated wood, and electronics. Treated wood is easy to miss, since old deck boards can look like plain lumber, so point it out when you book.
The regional landfill says it's illegal to throw electronic waste in the trash. TVs, computers, and microwaves go to its household hazardous waste area instead, at no charge.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. Mattresses are accepted, and appliances with refrigerant carry a per-item fee.
Ask your account manager about any item you're unsure of before it goes in.