Most building debris and household junk is fine. The limits come from Arizona law and from the city landfill's own refusal list.
Arizona bans lead-acid batteries from landfill disposal, and the state also bars operators from knowingly taking them. Waste tires are kept out of landfill disposal under state law as well, so keep both out of your container.
Cinder Lake Landfill will not take hazardous waste, untreated medical waste, radioactive waste, regulated liquid waste, car batteries, undewatered sludge, transformers and other oil filled electrical gear, universal waste, motor driven equipment, or friable asbestos. Lead based paint debris and anything from an environmental cleanup need written approval from the city before they arrive.
The usual bans apply on top of that list. No liquids, no paint, no solvents, no fuel, no oil, and no asbestos in a standard container.
It also helps to know the city's curbside bulk service will not take construction, repair, or demolition material, large auto parts, tires, used oil, or rocks, soil, and concrete. That is a big part of why a roll-off makes sense here. If you are unsure about one item, ask your account manager before it goes in.