Ordinary renovation and cleanout debris is fine. The limits come from California's disposal bans and from what the receiving facility will sort.
The California Department of Resources Recycling and Recovery keeps a long list of items banned from the trash. It covers batteries of every kind, fluorescent tubes and other lamps, latex and oil-based paint, solvents and paint thinner, pool chemicals, pesticides, motor oil and filters, antifreeze, and tires.
Electronics have their own path. Televisions, monitors, computers, printers, and phones are not trash in California, and neither are thermostats and other items holding mercury. Asbestos and chemically treated wood are out of a standard container as well.
That leaves plenty you can load: lumber, drywall, stucco, roofing, flooring, cabinets, furniture, carpet, and clean concrete and brick. Keep hazardous items in a separate pile for a county collection event, and ask your account manager about anything you cannot place.