Everyday construction and cleanout debris is welcome. The limits come from what the county's facilities will take and how each material is classified when it hits the scale.
Some items are handled as separate categories rather than trash. Lead-acid batteries and used motor oil come out of the load and go in free at any county facility when they're kept apart. Waste tires, oil filters, fluorescent tubes, light ballasts, and liquid paint are each charged and handled on their own.
Appliances need their refrigerant taken out before disposal, so a fridge, freezer, or window unit has to be declared rather than quietly buried under drywall.
Contaminated soil, asbestos, and industrial waste can only go to the county landfill and are refused at the transfer station on Grimes Avenue. Hazardous waste, liquids, solvents, and fuel are out of every container no matter where it goes.
One more thing worth taking seriously: the county charges a penalty when a load turns out to be a different type of waste than it was declared as. Run any questionable item past your account manager first.