Most building and cleanout debris is fine. The main limits come from California's list of household wastes that are banned from the trash.
CalRecycle's list includes all batteries, fluorescent tubes, LED bulbs, latex and oil-based paint, solvents, pesticides, pool chemicals, antifreeze, and motor oil and filters. Tires, asbestos, treated wood, propane tanks, and electronics are on the list too.
Hazardous waste, liquids, and fuel can't go in a standard dumpster either. Farm and garden chemicals are common in the valley, so keep pesticide and herbicide containers out of your load.
Some items are allowed at county sites for a separate fee. Tires and appliances like water heaters, washers, and refrigerators are priced per piece, so it pays to keep them apart from the rest of your debris.
Ask your account manager about any item you're unsure of before it goes in.