Most building and cleanout debris can go in your dumpster. The limits come from California's rules and from the facility that takes your load.
CalRecycle says it's illegal to put hazardous waste in the garbage anywhere in the state. Two items trip up remodeling jobs most often: asbestos in older building materials and treated wood with chemical preservatives, such as old fence posts and deck boards.
Tires aren't hazardous, but California still keeps them out of the trash to prevent mosquito breeding and tire fires.
The usual list applies too. Hazardous waste, liquids, paint, thinners, solvents, fuel, motor oil, antifreeze, pesticides, batteries, fluorescent tubes, electronics, and gas cylinders can't go in a standard dumpster.
If anything on your list seems uncertain, ask your account manager before you load it.