Most construction and cleanout debris is fine. The limits come from California's trash rules and the policies at the receiving facility.
CalRecycle keeps a list of items that are banned from the trash in California. It includes all batteries, fluorescent tubes, paint, solvents, and motor oil and filters. Antifreeze, tires, asbestos, and treated wood are also on the list. So are TVs, monitors, laptops, and other electronics, plus mercury items like old thermostats.
Also keep liquids, fuel, pesticides, and propane tanks out of your dumpster. Large appliances should be mentioned when you book so they can be handled properly.
CalRecycle points residents to their local household hazardous waste facility for these items, so set them aside before you start loading.
If you're unsure about something, ask your account manager before it goes in.