Most remodeling and cleanout debris can go in a container. California's trash rules and the disposal site that takes your load set the limits.
CalRecycle says it's illegal to put hazardous waste in the garbage. In California, that list includes every kind of battery, fluorescent bulbs, paint and paint thinner, pesticides, motor oil, antifreeze, and propane tanks. It also covers TVs, monitors, laptops, and other electronics. Tires are banned from the trash too.
Some building materials fall under the same rules. Asbestos and wood treated with chemical preservatives must be handled as hazardous waste, so they can't go in a standard dumpster. Liquids, solvents, and fuel are out as well.
Keep needles and medical waste out too. Mattresses and appliances can carry their own disposal fees, so mention them when you book.
If you're unsure about an item, ask your account manager before you load it.