Most construction debris and household junk can go in your container. California's trash rules and the landfill's own limits decide the rest.
California keeps a long list of household items out of the trash. CalRecycle's banned items list includes all batteries, fluorescent tubes, paint, solvents, pesticides, antifreeze, motor oil and filters, and tires. It also covers asbestos, propane tanks and other gas cylinders, and treated wood such as old fence posts and decking.
Electronics are banned from the trash too. TVs, monitors, laptops, printers, microwaves, and cell phones need to go to e-waste recycling instead of your dumpster.
As always, hazardous waste, liquids, and fuel stay out. The county runs household hazardous waste collection centers for chemicals, paint, and batteries.
Treated wood is a special case. Bowerman takes it only through a separate commercial process, so it can't ride along in a mixed load. If you're pulling out an old deck or fence, tell your account manager so they can plan for it.