Almost all Huntington Park construction and household debris is accepted. The limits come from California's disposal rules and from what the transfer station will take at the gate.
Keep hazardous waste out. That covers paint, solvents, fuel, used oil, pool chemicals, pesticides, and anything corrosive. Liquids of any kind are out, and so is asbestos. Treated wood and tires both have their own routes in California and cannot ride in a standard container.
The transfer station that serves this area is blunt about it: it takes only non-hazardous municipal solid and inert waste, and hazardous and liquid waste are not accepted at all. A single sealed bucket of old paint can hold up a whole load, so pull that material out before we arrive.
Electronics, batteries, appliances with refrigerant, and mattresses should be set aside and mentioned when you book, because they are handled separately rather than tipped with the rest. The City's code also treats asbestos, auto bodies, tires, used motor oil, and sludge as special wastes that need their own handling.
If you are holding something and you are not sure which pile it belongs in, ask your account manager before it goes in the container.