Most construction and cleanout debris is fine. The limits come from Texas landfill rules and from what the City landfill will accept.
The City landfill turns away hazardous waste, car and truck batteries, closed drums, explosives, hot loads, liquids, motor oil, oil filters, wet paint, and anything with PCBs. Friable asbestos needs at least 24 hours' notice and special handling.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either.
Refrigerators and air conditioners are taken, but only with written proof that the refrigerant has been removed. Tires go to the landfill's scrap tire area, so mention them when you book.
If you aren't sure about an item, check with your account manager first.