Ordinary household and construction debris is fine in a roll-off container. The limits come from Texas rules and from what each receiving site accepts.
Texas keeps hazardous waste out of municipal landfills completely, and treats industrial and special waste as separate categories needing state approval. Tires are barred unless they've been split, quartered, or shredded first, so they need their own route.
Paint, solvents, fuel, motor oil, antifreeze, pesticides, pool chemicals, and asbestos never belong in a container. Neither do batteries, fluorescent bulbs, ammunition, or appliances still holding refrigerant. The Cleburne transfer station turns all of those away at the gate, and it isn't alone.
Burleson's curbside crews won't take construction debris either. The City's list of what they leave behind covers brick, concrete, dirt, rock, building materials, roofing materials, shingles, treated lumber, railroad ties, automotive parts, oil, and paint. That list is basically a description of a remodel, which is why a container is the practical answer.
Not sure where something belongs? Ask your account manager before it goes in the container.