Most building and cleanout debris is fine to load. The limits come from California waste rules and from what the Kern County landfill will accept.
The Shafter-Wasco Landfill doesn't take hazardous waste, liquids of any kind, hot ashes, firearms, explosives, or non-friable asbestos. Unsecured loads also pay more at the landfill, so loads need to be covered on the way in.
California doesn't allow TVs, computers, batteries, or fluorescent bulbs in regular trash. Keep those out of your container and recycle them separately.
Leave out paint, solvents, fuel, and friable asbestos as well.
The landfill does take appliances, tires, treated wood, and used motor oil, but those are handled apart from general debris. Mention them when you book.
If you're not sure about an item, ask your account manager before you load it.