Most construction and cleanout debris can go in a container. California's statewide rules set the main limits.
The state keeps a long list of household items out of the trash. CalRecycle's banned-from-trash list covers every kind of battery, fluorescent lamps, latex and oil-based paint, paint thinner and other solvents, aerosol cans that still hold product, pesticides, pool chemicals, motor oil, antifreeze, and propane tanks. Electronics like TVs, computers, monitors, and phones are on it too, along with mercury thermostats and treated wood.
Tires aren't hazardous, but California still bans them from the trash. Asbestos, fuel, and other liquids aren't allowed in a standard dumpster either.
The local recycling facility accepts standard debris only, and it turns away hazardous material. Take banned items out before you start loading.
When you're not sure about an item, check with your account manager first.