Most debris from a cleanout or remodel is fine. The limits come from Iowa's landfill rules and from what the receiving site accepts.
Iowa bans several items from landfills. Yard waste can't be landfilled, and neither can lead-acid batteries like the ones in cars and mowers. Used oil and oil filters are banned as well. Tires can't go in whole, since the state only lets landfills take tires that have been processed.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos are also off limits in a standard dumpster.
Appliances need their own plan. In Johnston, curbside appliance pickups are scheduled through Metro Waste Authority, so mention any washers, fridges, or water heaters when you book. Brush and branches go to the City's yard waste program instead of the container.
If you're not sure about an item, ask your account manager before you toss it.