Nearly all East County renovation and household debris loads without trouble. The limits come from California rules and from the receiving landfill's own gate conditions.
The landfill requires that cathode-ray tubes, televisions, appliances, universal waste, electronic waste and household hazardous materials are all properly dealt with before the load arrives. In practice that means screens, monitors, fridges, batteries, fluorescent tubes and anything chemical come out of the container first.
Paint, solvents, thinners, fuel, motor oil, pool chemicals, pesticides and asbestos-containing material stay out as a matter of course, along with liquids of any kind. In mid-century La Mesa housing, asbestos can turn up in old floor tile adhesive, pipe lagging and textured ceilings, so a pre-demolition test is the right step rather than a loading decision.
Tires are kept separate as well, and the landfill randomly checks arriving vehicles for hazardous material, so a hidden item is likely to be found rather than overlooked.
If something is on the edge of those lists, ask your account manager before it goes in. It is a short conversation and it avoids a rejected load.