Most household and remodeling debris is fine. The limits come from California's trash bans and from the rules at the transfer station.
California makes it illegal to put hazardous waste in the trash. That covers batteries, fluorescent tubes, paint, solvents, pesticides, motor oil and filters, and propane tanks. Electronics like TVs, laptops, and monitors are banned from the trash as well. Tires are banned too, even though they aren't hazardous.
Two building materials need extra care. Asbestos can show up in older roofing, flooring, and siding. Wood treated with chemical preservatives must be handled as hazardous waste. Liquids, fuel, and asbestos can't go in a standard dumpster.
The City's own bins turn away liquid waste, tires, and universal waste. Fridges and mattresses can cost extra at the transfer station.
If you're not sure about an item, ask your account manager before you load it.