Most remodeling and cleanout debris can go in your container. The limits come from California's statewide trash bans and from what the landfill will take.
CalRecycle's banned-from-the-trash list covers more than most people expect. All batteries, fluorescent tubes, and mercury thermostats are on it. So are latex and oil-based paint, pesticides, pool chemicals, motor oil, antifreeze, and tires. Electronics such as TVs, monitors, laptops, printers, microwaves, and cell phones can't be thrown away either. Propane tanks, asbestos, and treated wood round out the list.
The Olinda Alpha Landfill posts its own list of refused items. It includes treated wood, asbestos, batteries, chemicals, fuel tanks, tires, paint, and liquid waste.
Standard dumpster rules apply as well, so keep out hazardous waste, liquids, solvents, and fuel. Tell your account manager about anything you're unsure of before it goes in.