Most household junk and building debris can go in your container. The limits come from California's rules on hazardous waste and from what the receiving facility will take.
California makes it illegal to put hazardous waste in the trash. That list is longer than many people expect. It covers every kind of battery, fluorescent tubes and bulbs, propane tanks, and aerosol cans that still hold paint or other chemicals. It also includes electronics like TVs, monitors, computers, and printers.
Two items catch remodelers off guard. Treated wood, such as old fence posts and deck framing, has to be handled as hazardous waste. So do older caulk and fluorescent light ballasts that may contain PCBs.
As with any dumpster, liquids, paint, solvents, fuel, and asbestos can't go in either. You can find the full state list on the CalRecycle banned from the trash page.
If you're not sure about something, ask your account manager before you toss it.