Most construction and cleanout debris is fine. The limits come from California's rules on hazardous waste and from the facility that takes the load.
CalRecycle says it's illegal to dispose of hazardous waste in the garbage. That covers batteries and fluorescent and LED lights, paint and solvents, pool and garden chemicals, antifreeze, motor oil and tires, asbestos, treated wood, gas cylinders, electronics, and anything with mercury.
The City's bulky item program won't take construction material, tires, or car and boat parts either. Residents can drop off batteries and fluorescent bulbs at no charge at E-Recycling of California, 7230 Petterson Lane in Paramount, and the City points people to household hazardous waste roundups for the rest.
Check with your account manager about anything you're unsure of before it goes in.