Most debris from a remodel or cleanout can go in the container. California rules and the county landfill set the limits.
California doesn't allow whole tires to be buried in a landfill unless they've been shredded first, so keep tires out of your container. The state also treats electronics, batteries, and fluorescent tubes as universal waste that can't go in the trash.
Tulare County's list of items spells out what its landfills turn away. That includes televisions, computers, printers, microwaves, cell phones, batteries, fluorescent lights, treated wood, friable asbestos, liquid waste, grease, and contaminated soil. Refrigerators and freezers are accepted only with the doors removed, and they carry an extra charge.
Paint, solvents, fuel, and other hazardous waste stay out as well. If you're not sure about an item, your account manager can check before you load it.