Most construction and cleanout debris is fine to load. California's rules and the facilities receiving your load set the limits.
CalRecycle lists many wastes banned from the trash. They include fluorescent tubes, all kinds of batteries, TVs, monitors, computers, and microwaves, plus motor oil, antifreeze, and tires. Asbestos, chemically treated wood, propane tanks, and aerosol cans that aren't empty are on the list too.
Hazardous waste, liquids, paint, solvents, and fuel can't go in a standard dumpster either.
Riverside County also limits some items at its landfills. The county takes no more than four appliances and five tires per homeowner per day, and it won't accept appliances or tires from businesses.
Before you load anything you're unsure about, check with your account manager.