Nearly everything from a typical remodel or cleanout can go in. California's rules and the transfer station set the exceptions.
California's Department of Toxic Substances Control treats a set of household items as universal waste. None of them can go in household trash or a landfill. That covers batteries, electronics, TVs and computer monitors, fluorescent bulbs and tubes, mercury thermostats, aerosol cans with product left in them, and solar panels.
Hazardous waste, liquids, paint, solvents, fuel, motor oil, and asbestos stay out of a standard dumpster too. The Devlin Road station takes small amounts of latex paint, used oil, antifreeze, and car batteries separately from its trash floor.
Tires and large appliances are charged by the piece at the station, so keep them out of your load and let us know about them. Mattresses have their own route through California's mattress recycling program, and the station accepts a couple of them at no charge when they come in on their own.
When you're unsure, ask your account manager before the item goes in the container.