Most construction and cleanout debris is fine. California's hazardous waste rules set the main limits, and they're stricter than in many states.
The state bans a long list of items from the trash. That includes every kind of battery, from AA cells to car batteries, plus fluorescent tubes and LED lamps, oil-based and latex paint, solvents, pesticides, antifreeze, motor oil and filters, and aerosol cans that aren't empty. Tires are banned from the trash too.
Standard exclusions apply as always. Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a dumpster.
One local item catches people out. Pressure treated wood and railroad ties count as hazardous waste in California, and only certain facilities can accept them, so keep that lumber out of your container.
Anything you're unsure about is worth a quick question to your account manager before it goes in.