Most household and construction debris can go in the container. California's disposal rules and the certified facilities set the limits.
CalRecycle lists items that are banned from the trash in California. They include all batteries, fluorescent tubes, paint, solvents, motor oil and filters, antifreeze, propane tanks, and electronics like TVs, monitors, and microwaves. Tires are banned too.
Two building materials need extra care. Asbestos, found in some older flooring, siding, and roofing, can't go in a standard dumpster. Treated wood, like old fence posts and deck framing, must be handled as hazardous waste under state rules.
Liquids and fuel are also off limits. If you're unsure about an item, check with your account manager before it goes in.