Ordinary construction and cleanout debris is welcome. The exclusions come from California law and from what the region's processing facilities will take.
California classifies several household items as universal waste, kept out of landfills by rule. Fluorescent tubes and lamps, batteries, and mercury switches and thermostats are all on that list, and older valley homes tend to produce all three during a remodel.
The city and county take those items at their free collection events instead. Their published list includes antifreeze, paint, paint thinner, turpentine, motor oil, oil filters, brake fluid, cleaners with acid or lye, pool chemicals, fertilizers, pesticides, batteries, and fluorescent bulbs, none of which belongs in a container.
A few things go nowhere easily. Ammunition, explosives, and biohazardous waste are refused at the collection events, and Los Angeles County notes that solar panels are not accepted at its temporary events or permanent centers at all.
Large appliances also need declaring rather than loading, and asbestos in an older building calls for abatement, not a roll-off. Ask your account manager about anything you're unsure of.