Most house and job-site debris is fine. The limits come from Arkansas rules and from what the county landfill will take.
Whole tires are out. Arkansas keeps them out of landfills unless they've been cut up or shredded, and burning, burying, or dumping them is against the rules. The state's own guidance sends them to a licensed tire collection point instead.
Lead-acid batteries are out too. The state says plainly not to put them in the garbage or burn them, and to take the cores to a battery dealer, a collection center, or a recycler.
Hazardous material of any kind stays out of the container: solvents, fuel, motor oil, pool chemicals, pesticides, antifreeze, propane tanks, and anything with asbestos in it. Liquids are a problem on their own, since a leaking load can be refused at the scale.
Paint is the common local question. Jonesboro's own guidance is to dry it out first, by stirring in kitty litter, newspaper, or sand and leaving the lid off for a couple of days. Once it's solid, it can go with the load.
Still unsure about something? Run it past your account manager before it goes in.