Most construction and household debris can be loaded. The limits come from the state disposal bans and from what the receiving facility accepts.
Massachusetts bans a list of materials from being thrown away or sent for disposal, and the rule binds whoever hauls the load as well as whoever filled it. MassDEP's list includes asphalt pavement, brick and concrete, clean gypsum wallboard, ferrous and non-ferrous metals, glass, metal and plastic containers, lead acid batteries, leaves and yard waste, mattresses, recyclable paper and cardboard, textiles, white goods, and old tube televisions and monitors. Wood and whole tires are barred from landfills.
Those materials can still go out in a container. They are separated at a processing facility instead of buried, which is why a clean load of one material often costs less to move than a mixed one.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos are never allowed in a standard container. The Town's transfer station also turns away hazardous waste, brush, and leaves, so those need their own route.
Anything you are unsure about is worth a quick question to your account manager before it goes in the container.