Most debris from a remodel or cleanout can go in. The limits come from California's list of wastes banned from the trash and from county landfill rules.
According to CalRecycle, the banned items include all batteries, fluorescent tubes, LED lights, latex and oil-based paint, paint thinner, aerosol cans that aren't empty, pool chemicals, and pesticides. Antifreeze, motor oil and filters, tires, treated wood, asbestos, and propane tanks are on it too. So are TVs, computers, cell phones, and other electronics, plus mercury items like old thermostats.
Hazardous waste, liquids, solvents, and fuel can't go in a standard dumpster either. Kern County takes tires and treated wood at its sites as separate items with their own fees, so set them aside and mention them when you book.
Ask your account manager about anything you're unsure of before you load it.