Most remodeling and cleanout debris is fine. The limits come from California's trash bans and from the rules at the landfill that takes your load.
California's recycling agency, CalRecycle, keeps a list of waste banned from the trash. It covers every kind of battery, fluorescent tubes, TVs, monitors, computers, and printers. It also covers motor oil and filters, antifreeze, latex and oil-based paint, solvents, and pesticides. Asbestos, treated wood, and tires are on the list, too.
Hazardous waste, liquids, fuel, and propane tanks can't go in a standard dumpster either.
Many of those items have a local drop-off. The City's household hazardous waste facility at 8794 Lion Street is open Saturdays from 8 a.m. to noon for San Bernardino County residents. It takes paint, batteries, TVs, monitors, and motor oil. It won't take tires, asbestos, or business waste, so plan a separate route for those.
If you're unsure about an item, ask your account manager before it goes in the container.