Most remodeling and cleanout debris is fine to load. California's disposal rules and the transfer station that takes your load decide the rest.
California doesn't allow hazardous waste in the trash. CalRecycle's list of waste banned from the trash covers every kind of battery, fluorescent tubes and LED bulbs, paint, solvents, pesticides, motor oil and filters, antifreeze, and tires. It also includes TVs, computers, phones, microwaves, and anything with mercury, like old thermostats.
Asbestos, treated wood, and compressed gas cylinders are on the state list too. Liquids, fuel, and car parts like engines or fuel tanks don't belong in a dumpster either.
Some bulky items are allowed but cost extra. Mattresses, washers, stoves, and refrigerators are usually charged by the piece, so list them when you book.
When you're unsure about something, your account manager can check before it goes in the container.