Check shutter speeds - Does the shutter fire at all shutter speeds? Look particularly for a slowing of the shutter speeds, which will be most noticeable at the lower and higher speeds.
Check meter accuracy - Use another camera for comparison, but keep in mind that very few cameras will be exactly the same.
Check lens aperture - Make sure that it stops down all of the way. It should be lightning quick. There should be no oil on the blades.
Check the aperture coupling pin (if applicable) - It should move smoothly and quickly.
Check focus - Make sure that your camera will focus at both the minimum focus distance and at infinity. The focus ring should move smoothly but not be loose.
Check the cosmetics - Look for dings, dents, scratches, and I.D. numbers that have been engraved into the equipment (they reduce the value).
Check for water damage - Look for rust, corrosion, and water spots in the lens. Remember to smell the equipment for mold or mildew.
Check the battery compartment - Look for cracks or corrosion.
Check the flash sync - make sure the flash fire and the shutter speed is opening correctly.
Check the lens - Look for scratches, fungus, mildew, fog and separation.
Check the self-timer
Check the ISO dial (ASA in older models) - Make sure that it turns easily and that it actually affects the light meter.
Check the film counter - Does it reset?
Battery availability - Some of the older-style batteries are no longer manufactured or have been banned because of their contents.