Most building and household debris loads with no trouble. The limits come from Michigan's rules and from the City's own instructions.
Michigan keeps a firm list out of every landfill in the state. That list covers deposit containers, yard waste, used oil, bulk liquids, whole tires, empty drums, hazardous waste, lead acid batteries and low-level radioactive waste. Asbestos, material containing PCBs and septage need special handling and approval before any landfill will take them.
The City is blunt about hazardous material: never set it at the curb. Its own examples include bathroom cleaners, batteries, furniture polish, lawn and garden chemicals, old computers, paint, pesticides, shellac, stains, transmission fluid, turpentine and used motor oil. Wayne County runs the drop-off program for all of that, and the coordinator can be reached at 734-326-3936.
Yard waste is worth flagging separately. Michigan bars it from landfills, and the City collects it on its own schedule through the growing season, so it does not belong in the container. If an item has you guessing, ask your account manager before it goes over the side.