Check the underside for gouges, scrapes, dents in the fluid pans or gas tank. All can indicate rough service or a lot of gravel road time. Scrapes and dings underneath can open the way for rust.
Check tires for uneven wear, cupping, which may indicate wheel alignment or bearing problems.
While you are looking under the hood, salvage yard parts commonly have the make, model, and year of the vehicle written on them in yellow or white paint marker. This might indicate a collision or other damage the owner might not be forthcoming about.
Also, look around inside the car, under the hood, and in the trunk for accumulations of dried mud in places you wouldn’t expect it to be that might indicate flood damage. Ideally, you would want to lift the carpet to see what’s underneath, especially if you detect a musty smell anywhere. A musty smell can also indicate leakage around windows or doors, or a plugged drain in the AC system.