Most construction and household debris can go in a dumpster. California's disposal rules and the facility that takes your load set the limits.
CalRecycle says it's illegal to throw hazardous waste in the trash because it can harm health and cause fires. The state list covers batteries of every type, fluorescent tubes, LED lights, TVs, computers, monitors, and printers. It also covers latex and oil-based paint, aerosol cans that aren't empty, motor oil, antifreeze, pesticides, and pool chemicals.
Several items on that list show up in home projects. Treated wood has to be handled as hazardous waste. Tires, propane tanks, and asbestos can't go in either. Liquids, solvents, and fuel are also off limits in a standard dumpster.
West Covina adds one more step for older buildings. Before demolition, any building from before 1970 has to be surveyed by a licensed inspector for hazardous materials.
If you're unsure about an item, ask your account manager before you load it.