Nearly all remodeling and cleanout debris can go in your container. The limits come from South Carolina's landfill rules and from the landfills that receive the load.
South Carolina doesn't allow used motor oil in household waste. Tires, car batteries, yard trash, and large appliances such as refrigerators and washers follow separate disposal rules. Computers, monitors, printers, and TVs can't be sent to a landfill at all.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos also can't go in a standard dumpster.
The Town's trash service page lists what its crews won't pick up, and the list is a good guide. It includes engine parts, old pesticides, creosote railroad ties, oil, tires, batteries, wet paint, tree stumps, bricks, and concrete. Fluorescent bulbs also stay out because they contain mercury. Bricks and concrete can go in a roll-off, but most of the other items need a special drop-off.
If you're unsure about an item, check with your account manager before it goes in.