Most of what comes out of a remodel or a cleanout can go straight into the container. Wood, drywall, flooring, cabinets, furniture, and general junk are all fine.
California keeps a longer list of banned items than most states. CalRecycle says it's illegal to put hazardous waste in the garbage, and the state's banned list covers fluorescent tubes and lamps, every size of battery, motor oil and filters, antifreeze, tires, pesticides, aerosol cans that aren't empty, propane and other gas cylinders, treated wood, and electronics.
That rules out the usual suspects in any dumpster: hazardous waste, liquids, paint, solvents, fuel, and asbestos. Keep them out of the container and they won't hold up your haul.
Goleta gives you other routes for the rest. Single-family homes get four free bulky item collections a year, five items each, and free pickup for electronics and old appliances, though the bulky item program won't take construction or remodel material. Paint, batteries, and tubes go to the Community Hazardous Waste Collection Center at UC Santa Barbara, which serves residents on weekends.
When an item has you guessing, your account manager can confirm whether it can ride along before you load it.