Most construction and household debris loads without trouble. The limits come from Oregon's landfill bans and from the regional facility that receives your load.
Oregon makes six things illegal to send to a disposal site, and the state's environmental quality department lists them as discarded vehicles, large home or industrial appliances, used oil, tires, lead-acid batteries, and computers, monitors and televisions. Keep all of those out and route them separately.
The regional transfer stations add their own refusals. They will not take asbestos-containing material, burned material or wildfire ash, flat or built-up roofing, loads of liquids, petroleum-contaminated soil, or electric vehicle batteries. Flat roofing is the one that catches contractors out, so flag a torch-down or built-up tear-off when you call.
Asbestos deserves extra care on older Forest Grove houses. Metro now asks every customer for documentation about asbestos, and a load that turns out to contain it can leave the customer paying for testing and removal.
Hazardous waste, liquids, paint, solvents and fuel stay out of every container. The City does not run a hazardous waste drop-off of its own, so those need a regional collection event. Ask your account manager about anything you are unsure of before it goes in.