Everyday building and household debris is fine. The limits come from Iowa law and from what the receiving plant will take.
Iowa bans burying yard waste, lead acid batteries and waste tires. Yard waste can still go to a landfill when it is separated at the source for composting, which is why grass and branches belong in their own pile rather than mixed into a cleanout load. Batteries and tires have to be routed to a recycler.
Hazardous waste, liquids, paint, solvents, fuel and asbestos cannot go in a standard container either.
A few things are allowed but priced separately. The Ames plant charges per item for appliances, televisions, monitors, mattresses, couches, hot tubs and tires, and it accepts over-the-scale and construction loads at its own discretion based on the material. That makes it worth naming the oddities up front.
When you are not sure about an item, ask your account manager before it goes in the container.