Most construction and cleanout debris is fine. The limits come from California's disposal rules, from the city code, and from what the facility will take at the gate.
California makes it illegal to put hazardous waste in the trash. The state's banned items list covers paint, solvents, pesticides, pool chemicals, aerosols, propane cylinders, electronics, every type of battery, fluorescent and LED lamps, and tires.
Treated wood is the big one on a Santa Cruz job. California handles it as hazardous waste, so pressure-treated decking, fencing, railroad ties, and pilings all need separate handling rather than a spot in the container.
The city code also bars volatile materials like gasoline and alcohol, hazardous waste, infectious waste, sludge, and toxic waste from any load going to the city facility. Noxious items like ash, loose fiberglass, sawdust, and kitty litter need their own handling too.
The City's container guide lists asbestos, mattresses, TVs, computers and monitors, batteries, fluorescent tubes, appliances, and oil filters as special handling items. It also notes that state law requires construction and demolition material to be recycled, which is a good reason to sort. If something has you unsure, ask your account manager before it goes in.