Most remodeling and cleanout debris is fine to load. The limits come from California rules and from what the county landfill will take at the gate.
California is strict about what it calls universal waste. The state says no person or business may put it in the trash, and the list covers batteries, lamps, electronic devices, television and monitor tubes, mercury items, aerosol cans that are not empty, and solar panels. Those all need their own route, whatever else is going in the container.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos stay out of a standard dumpster. The county landfill also turns away sealed containers, hot ashes, medical waste and sharps, and many items containing mercury or lead. Refrigerators are accepted only with the refrigerant removed, tires come with limits, and treated wood is allowed.
Household chemicals from a garage cleanout have a separate home through the county fire district's hazardous waste program, reachable at 800-645-9228. When an item has you guessing, ask your account manager before it goes over the rail.