Most debris from a remodel or cleanout can go in your container. The limits come from California's trash bans and from what the landfill can take.
California keeps a long list of items out of the trash. CalRecycle names batteries of every kind, fluorescent tubes and other mercury lamps, paint and paint thinners, pesticides, pool chemicals, antifreeze, motor oil and filters, and propane tanks. Electronics are banned from the trash as well.
Two building materials are on the state list. Asbestos, found in some older roofing, flooring, and siding, needs special handling. Treated wood, such as old fence posts and deck lumber with chemical preservatives, can't go in a regular load. Tires are banned from the trash too.
Hazardous waste, liquids, and fuel are also off limits in a standard dumpster.
If you have an item you're unsure about, check with your account manager before it goes in.