Ordinary household and construction debris is fine. The limits come from Texas rules and from what the landfill will take at the gate.
Texas keeps hazardous waste out of municipal landfills completely, and it sorts industrial and special wastes into separate categories that need state approval before a landfill can accept them. Whole tires are out as well. The state allows tires only after they've been split, quartered, or shredded, so tires need their own route.
Paint, solvents, fuel, motor oil, pool chemicals, pesticides, and asbestos never belong in a roll-off container either. Neither do liquids of any kind, or appliances holding refrigerant, which have to be drained by a technician first.
The landfill has its own conditions on arrival. Every load has to be fully covered and tarped or a fee is added, and anyone stepping out of a vehicle on site needs a safety vest. Our drivers handle the tarping, which is one less thing on your list.
Not sure where an item belongs? Ask your account manager before it goes in the container.