Most building and household debris loads with no trouble. The limits come from Minnesota law, from Hennepin County, and from the City's own sites.
Minnesota law keeps yard and tree waste out of the trash, and the City says so plainly on its own pages. Grass, leaves, brush and tree waste all need the separate route, and Plymouth runs a free seasonal yard waste site for that. Propane tanks and other pressurized cylinders are barred from household trash and recycling too.
Hazardous material never goes in the container. That means paint, solvents, fuel, used oil, antifreeze, pesticides and pool chemicals, and it also means asbestos. Hennepin County's drop-off facilities handle most of those, but they take no garbage, construction material, remodeling debris, concrete, asphalt, carpet, furniture or wood, so the container and the County drop-off cover different halves of a remodel.
The City's own recycling site is stricter still. It is for Plymouth residents and small businesses only, it takes curbside recyclables and nothing else, and it is video monitored with a $700 fine for leaving trash, carpet, furniture or bulky items there. If an item has you guessing, ask your account manager before it goes over the side.