Most remodeling debris and household junk can go in. The limits come from Washington's solid waste rules and from what Spokane's disposal sites will accept.
Asbestos is a firm no. The City says asbestos materials aren't allowed at the Waste to Energy Facility or the county transfer stations, so any suspect siding, tile, or pipe wrap must be tested and handled by a licensed abatement crew.
Leave out hazardous waste, liquids, paint, solvents, fuel, and car batteries as well. Spokane residents can drop off household hazardous waste for free at the Waste to Energy Facility, so there's an easy option for leftover paint and chemicals.
A lot of building material can be recycled here, including concrete, asphalt, brick, wood, metal, and carpet. If you'd like to keep clean material separate, or you're unsure about anything else, ask your account manager before you load it.