Most household and construction debris is fine. California's statewide rules set most of the limits.
CalRecycle's list of wastes banned from the trash covers batteries of all kinds, fluorescent tubes and bulbs, latex and oil-based paint, solvents, pesticides, pool chemicals, motor oil and filters, antifreeze, and tires. It also includes asbestos, treated wood, propane and other gas cylinders, and electronics like TVs, monitors, computers, printers, and phones.
The usual dumpster rules apply too: no hazardous waste, liquids, fuel, or solvents.
Los Angeles County runs free household hazardous waste collection events, and Norwalk's recycling office can point you to the next one at 562-929-5511. Set those items aside before you start filling the container.
If you're unsure about anything, ask your account manager before it goes in.