Most remodeling and household debris can go in. The limits come from California's trash rules and from the sites that process your load.
CalRecycle keeps a list of waste banned from the trash in California. It includes batteries, fluorescent bulbs, paint, solvents, motor oil, antifreeze, and pesticides. Tires, propane tanks, and electronics like TVs, computers, and microwaves are banned too.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. Treated wood, like old fence boards, deck framing, and railroad ties, counts as hazardous waste in California. RecycleSmart notes that household hazardous waste sites can't take it, so plan a separate route for it.
For paint, batteries, and chemicals, Danville residents can use the Central Contra Costa Sanitary District's household hazardous waste facility in Martinez for free. Ask your account manager about anything you're unsure of before it goes in the container.