Most construction and cleanout debris is fine. The limits come from California's trash bans and from Miramar Landfill's rules.
California makes it illegal to put hazardous waste in the trash. CalRecycle's list covers every kind of battery, fluorescent tubes, electronics, paint, solvents, motor oil, antifreeze, and propane tanks. Tires are banned from the trash as well, and treated wood must be handled as hazardous waste.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster.
Miramar Landfill adds its own rule. TVs and other electronics, appliances, universal waste, and household hazardous materials must be handled properly before a load enters the landfill. Keep those items out of your container.
Your account manager can tell you whether an item is allowed before you load it.