Most construction and cleanout debris can go in your container. The limits come from California's trash rules and from the facilities that take your load.
CalRecycle lists the waste banned from the trash across California. That includes batteries, fluorescent tubes, paint, solvents, motor oil, antifreeze, and pesticides. Tires, propane tanks, and electronics like TVs, monitors, and microwaves are on the list too.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. Treated wood, such as old fence posts, patio beams, and railroad ties, must be handled as hazardous waste in California. Keep it out of the main load.
Pool chemicals and leftover paint need a separate drop-off. If you're unsure about an item, ask your account manager before it goes in the container.