Most of a remodel loads without a second thought: lumber, drywall, roofing, siding, flooring, cabinets, fixtures, carpet, and general junk. The limits come from Oklahoma's landfill rules and from what the receiving site refuses at the gate.
Oklahoma keeps hazardous, radioactive, and PCB waste out of permitted solid waste landfills, and regulated medical waste can only go to a facility licensed for it. Friable asbestos is barred unless a landfill's own permit specifically allows it, which is why asbestos work is always handled separately.
Metro landfills also refuse tires, electronic waste, appliances with Freon or other refrigerant, and household hazardous waste such as car batteries, motor oil, propane tanks, and pool chemicals. One of those items can hold up a whole load.
Liquids, paint, solvents, and fuel stay out of a standard container as well. Moore residents can take that kind of material to the Oklahoma City Household Hazardous Waste Collection Center, which accepts waste from Moore households and may bill the service through the city.
Pull the restricted items out before the container is loaded, and run anything you're unsure about past your account manager first.