Most of what a remodel produces is fine: framing, drywall, roofing, flooring, cabinets, trim, fixtures, carpet, and general junk. The limits come from Tennessee's rules and from Metro's own trash code.
Tennessee makes it illegal to put wet latex paint into a landfill. Dried latex can go, which is why the state tells residents to dry leftover paint with kitty litter or sawdust first. Oil-based paint cannot go in the trash at all, and lithium, nickel-cadmium, and nickel-metal hydride batteries have to be recycled rather than tossed.
The state also keeps whole tires, lead-acid batteries, and used oil out of disposal facilities, and every county has to provide a place that takes them.
Metro adds its own list. The City bans yard waste, cardboard, and electronic waste from the trash, so brush, flattened boxes, and old televisions need to be handled separately from your container.
Hazardous waste, liquids, solvents, fuel, and asbestos never belong in a standard dumpster. When an item has you guessing, check with your account manager before it goes in rather than risking a rejected load.