Most construction, remodeling, and yard debris is allowed. The limits come from California's trash bans and from what the processing facility accepts.
California law makes it illegal to throw hazardous waste in the trash. That includes batteries of every kind, fluorescent lamps, paint and paint thinner, pesticides, pool chemicals, antifreeze, and motor oil and filters. TVs, computers, and other electronics are also banned from the trash. Tires can't go in the trash either.
Some building materials need special handling. Asbestos may be in older roofing, flooring, siding, and cement products. Wood treated with chemical preservatives is handled as hazardous waste, and propane tanks are banned from the trash. Liquids and fuel can't go in a standard dumpster.
If you have something you're unsure about, ask your account manager before it goes in the container.