First, be aware that the bore will probably be dirty and dusty. This can either make it look worse, or mask real problems. Ask to have the barrel cleaned out. Most used rifles will have dirty bores. If the gunshop won't clean out the barrel, you probably don't want to buy a rifle there.
Look for a shadowy dark ring. This indicates the barrel may have a bulge in it. If it's bad, the bulge may also show on the outside too.
Look for pits or corrosion in the bore. While pitted barrels can shoot very well, you probably don't want it.
Dark areas in front of the chamber could be bore errosion,
OR might simply be metal fouling that can be removed.
Look inside the muzzle for wear on the ends of the rifling. Barrels that are cleaned from the front, often get worn by the cleaning rod.
Look at the chamber for scratches, corrosion, or pitting.
Most barrels sent back to custom rifle makers as no longer accurate, are first given a good cleaning. In a majority of cases, this is all thats wrong.
If you buy a used rifle, the FIRST thing to do is get GOOD, proper cleaning gear, and get ALL fouling out of the bore.