Most construction and household debris is fine to load. The limits come from the state disposal bans and from what the receiving facility accepts.
Massachusetts bars a long list of materials from being thrown away or sent for disposal, and the duty binds the hauler as well as the generator. MassDEP's list covers 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 tube televisions and monitors. Wood and whole tires are barred from landfills.
Those materials can still leave in a container, because the load is sorted at a processing facility. It is why keeping concrete, brick, or clean wood in a single-material load often costs less than mixing everything together.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos never go in a standard container. Quincy runs its own household hazardous waste drop-off days at the Public Works yard on Sea Street for residents only, and the City states plainly that the event is not for commercial disposal and takes no asbestos, tires, or latex paint.
One more local rule is worth knowing: the City code bars bringing waste into Quincy from outside the city for disposal here. If you have an item you are unsure about, ask your account manager before it goes in.