Everyday renovation and household debris gives no trouble at all. Wood, drywall, flooring, cabinets, roofing, furniture, carpet and packaging all load normally.
Hazardous material is the hard line everywhere in Michigan. Liquids, fuels, solvents, oil-based paint, pesticides, pool chemicals, asbestos and anything under pressure stay out of a container, whatever the receiving site. Southfield's own code separately bars burying waste, burning it in the open, and letting waste scatter from a container onto a street or a neighboring lot.
Items that need a different route rather than a container include tires, car batteries, refrigerant appliances, fluorescent tubes, televisions and computer monitors. Southfield is a member community of the Resource Recovery and Recycling Authority of Southwest Oakland County, which runs drop-off recycling and household hazardous waste collection events for residents of its nine member communities. That is a residents' service, not a commercial disposal route, so a contractor clearing a site should plan a separate arrangement for those items.
If you are not sure whether something is acceptable, tell your account manager what it is before loading. Declaring an awkward item in advance is far cheaper than having a full container refused at the gate.