Most construction and household debris is fine. The limits come from Texas rules and from the city transfer station that receives the load.
Texas bars nine categories from municipal landfills. The ones that come up on a job site are lead acid batteries, do-it-yourself used motor oil, used oil filters, liquid waste, and hazardous waste. Whole tires are out too, unless they have been processed: the state says scrap tires may be landfilled only if split, quartered, or shredded. Refrigerators and freezers are not banned outright, but the refrigerant has to be reclaimed by licensed personnel before they can be taken.
The transfer station adds its own list and it is stricter than the state's. It will not take paint, chemicals, lead, explosives, liquid waste, grease trap waste, septic pumpings, medical waste, or anything containing asbestos. Brush and yard waste are not accepted there either; those go to the compost site on its own schedule.
Container rules spell out a few more. Dead animals, brush, yard waste, loose tires, and appliances that still hold refrigerant are not allowed in a roll-off, and anything unauthorized found in a container gets pulled out before service or returned to you afterward.
If something on your list is borderline, ask your account manager before it goes in.