Most household and construction debris loads without any trouble. The limits come from Texas disposal rules and from what the receiving landfill will accept.
Texas keeps a short list of items out of every municipal solid waste facility in the state. Lead-acid batteries, do-it-yourself motor oil, used oil filters, and whole tires are all barred. So are refrigerators, freezers, air conditioners, and anything else holding chlorinated fluorocarbon coolant. Liquid waste is out as well.
Hazardous waste, paint, solvents, fuel, and asbestos can't go in a standard container either.
Electronics need care. The Texas Commission on Environmental Quality notes that discarded TVs and computer monitors may count as hazardous waste and asks that used electronics be recycled instead. Set them aside before loading day.
The type of landfill matters too. A construction and demolition landfill can take brush, building debris, and similar material, but not household waste, so a mixed load has to go to a full municipal landfill. Your account manager will sort out which one fits your debris.