Most debris from a remodel or cleanout can go in. California's trash rules and the transfer station's limits set the rest.
CalRecycle's list of items banned from the trash includes all batteries, fluorescent tubes, LED bulbs, and electronics such as TVs, monitors, laptops, and printers. Tires, propane tanks, and other gas cylinders are on the list too.
Wood treated with chemical preservatives, like old deck framing, has to be handled as hazardous waste. So does asbestos, which shows up in some older roofing, flooring, and siding.
Hazardous waste, liquids, paint, solvents, and fuel can't go in a standard dumpster. South Lake Tahoe is also bear country, and the City warns that garbage is a leading cause of trouble with bears. Keep food waste out of an open container.
If you're unsure about an item, ask your account manager before it goes in.