Most debris from a remodel, a build, or a cleanout is fine to load. California's rules on household hazardous waste set most of the limits.
CalRecycle lists several everyday items that can't go in the trash anywhere in the state. These include all batteries, fluorescent tubes and other lamps, household and garden chemicals, oil-based paint, motor oil, antifreeze, and tires. Propane tanks and other gas cylinders are on the list too, along with wood treated with chemical preservatives.
Electronics need special care. The state treats broken TVs, monitors, laptops, and tablets as hazardous waste, so they go to an e-waste recycler, not a dumpster.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either. Asbestos can turn up in older roofing, flooring, and siding, so have it checked before a tear-out.
If you have a question about any item, your account manager can give you an answer before it goes in the container.