Most debris from remodels and cleanouts can go in your container. The limits come from South Dakota law and from the City landfill's own rules.
State law says no landfill in South Dakota may accept yard waste, lead acid batteries, waste motor oil, or large appliances for disposal. Tires can't be buried either unless they've been processed first. Pull those items out before you load.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. The Watertown landfill does take some of these materials in separate loads. It accepts electronics, major appliances, and clean wood at a lower per-ton rate, and asbestos only as its own load at a higher rate.
If you're unsure about an item, ask your account manager before you toss it in.