Ordinary construction and cleanout debris is fine. The hard limits come straight from what the county landfill will bury.
The landfill's refusal list is short and strict. Nothing hazardous, no liquids of any type, no car batteries, no lithium batteries, and no electronics go in the cell. Appliances holding coolant, including refrigerators, freezers, air conditioners, and dehumidifiers, are only accepted with a certified refrigerant reclamation form.
Larger propane tanks are out, though small camping cylinders are allowed. Gas tanks and sealed drums are refused unless they have been triple washed and either drilled or had the lids removed, so staff can see they are empty.
Electronics have a way around this. The same site takes computers, televisions, printers, copiers, and similar gear for recycling at a per item rate, which is why pulling them out of the container is the easy move rather than a problem.
Paint, solvents, fuel, and asbestos all stay out of a standard container. If you are not sure about an item, describe it to your account manager before it goes in.