Most construction and cleanout debris is fine to load. The limits come from California's list of wastes banned from the trash and from the landfill's own rules.
CalRecycle's list includes all batteries, fluorescent tubes, LED lights, latex and oil-based paint, solvents, pool chemicals, pesticides, antifreeze, and motor oil and filters. It also covers tires, asbestos, treated wood, propane tanks, and electronics such as TVs, laptops, printers, microwaves, and cell phones.
Hazardous waste, liquids, and fuel can't go in a standard dumpster either. The City's own code also keeps paint, solvents, pesticides, and fuel out of regular trash pickup.
If you're not sure about an item, ask your account manager before it goes in.