Ordinary household and construction debris is fine. The exceptions come from hazardous waste rules and from what the landfill will take at the gate.
Salina runs a household hazardous waste facility, and its accepted list doubles as the list of what should never go in your container. That covers aerosols, automotive fluids, antifreeze, fuel, used oil, button cell and lithium and rechargeable batteries, fluorescent tubes and compact bulbs, herbicides and pesticides, household cleaners, mercury thermometers and thermostats, oil based and latex paint, small propane cylinders, and wood stains.
Asbestos is handled separately and goes through the landfill itself rather than the hazardous waste facility. Electronics have their own route too, with the City running a collection event each May, so televisions, monitors, and computers should be set aside rather than loaded.
The facility does note one practical exception. Empty containers and latex paint that has fully hardened can go out with ordinary trash once the lids are off.
Tires belong with a tire dealer or a licensed collection site, not in a container. If you are unsure about an item, ask your account manager before it goes in.