Most household and building debris is fine. The limits come from New York law and from what the receiving station is permitted to accept.
New York bans electronics from the trash outright. Since 2015, covered electronic equipment can't go to the curb, into a landfill, or into a waste-to-energy plant, and the state can fine a hauler or a disposal facility for each violation. That's why a television in a container is a real problem rather than a minor one.
Batteries are banned too, in two separate ways. It's illegal to put spent lead-acid batteries, the kind in cars and mowers, in the trash, and a retailer has to take up to two a month from you free of charge. New York separately bars covered rechargeable batteries, including lithium ion and the packs out of e-bikes and scooters, and a retailer that sells them has to take back up to ten a day.
Whole tires can't be buried under New York's tire law, and a tire shop has to accept your old tires when it sells you new ones. Hazardous waste, liquids, paint, solvents, and fuel stay out of a standard container as well.
Three categories matter especially here because the station that receives Troy's waste isn't permitted for them: electronics, household hazardous waste, and yard waste. All three have to come out before the container leaves, or the load gets turned away at the gate. New York also requires a container like ours to travel enclosed and completely covered, so loading level rather than heaped is part of the deal. Anything you are unsure about is worth a quick word with your account manager first.