I would check the inside of the tire to look for belt damage/cracks in the rubber, as well as the sidewall for anything that looks like it rubbed against a curb.
Most people seem to neglect checking the manufacture date on the tire. It's usually 4 digits circled (ex: 3409) where the "34" means the 34th week and the "09" is the year 2009. There are a lot of used tires for sale where they are 8, 10 years old but still have a ton of tread left but as a tire ages, the materials also deteriorate. Normally tires should be changed every 6-7yrs. It's also a good way of knowing whether an owner has possibly replaced 1 or more tires in a pair/set.
It'll look something like this: