Ordinary home and construction debris is fine. The limits come from Tennessee's rules on hazardous household material and from what the receiving facility will accept.
Tennessee steers five categories away from the trash: batteries, oil, paint, antifreeze, and electronics. Those go to a collection center instead, since they can do real harm if they end up buried. Televisions, monitors, and computers belong in that group, so pull them before the container leaves.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos are out of every container we place. So are hot ashes and anything that could catch. Tullahoma's own code makes burning material in a container, or loading anything combustible or volatile into one, an offense.
Painted and pressure treated wood has its own path in this area. Franklin County will not take it at a county site and sends it to the transfer station instead, which is where your container goes anyway, so it can ride along with the rest of the load.
Tires, appliances, and anything with a compressor should be called out when you book. Ask your account manager about a questionable item before it goes in rather than after.