Massachusetts has one of the longest disposal ban lists in the country, and it reaches the hauler as well as the customer, so this section matters more here than in most places.
The state bans these materials from disposal and from transport for disposal: asphalt pavement, brick and concrete, cathode ray tubes, clean gypsum wallboard, commercial food material, ferrous and non-ferrous metals, glass and metal and plastic containers, lead-acid batteries, leaves and yard waste, mattresses, recyclable paper and cardboard, textiles, treated and untreated wood at landfills, large appliances, and whole tires at landfills.
That doesn't mean those materials can't go in a rented container. It means the load has to be taken somewhere that sorts and processes it instead of burying it, which your account manager arranges when you book.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos stay out of every standard container, along with propane tanks.
The City's own site charges separately for several of these items at its drop-off area, including $25 for a car tire and $35 for a mattress. Set those aside and mention them when you book so they can be handled properly.