Most construction and cleanout debris can go in your container. The limits come from California's rules and from the landfill that takes your load.
CalRecycle, the state's recycling agency, keeps a long list of items that can't go in the trash. It includes all batteries, fluorescent bulbs, electronics, paint, solvents, pesticides, motor oil and filters, antifreeze, tires, and propane or other gas cylinders. Asbestos and wood treated with chemical preservatives are on the list too.
Along with those, keep hazardous waste, liquids, paint, solvents, fuel, and asbestos out of a standard dumpster.
The Kiefer Landfill asks customers to drain fluids like gas and oil and pull out removable batteries before disposal. Items with built-in batteries have to go to an electronics recycling program instead.
If you're unsure about something, ask your account manager before you load it.