Things to look for are excessive copper fouling, like copper plating that won't easily clean out. Usually caused from deep machining marks in the throat or button chatter on factory grade barrels (Savage is a big offender here, but not alone).
Can also look for uneven rifling start, and/or off-center free-bore. Doesn't necessarily mean anything, but something to look for if accuracy can't be fixed. Indicative of a bad indicating job on the manufacturer's part.
Obvious defects in the rifling, bulges, flattened lands, etc... Can sometimes cause issues. Internal burrs, especially on AR's where there's a gas port...
Totally roached burned out firecracked throats. This is a slow process and it shows up usually around 500-1000 rounds into a barrel and just keeps getting worse. When accuracy/velocity drops off is totally dependent on caliber, rate of fire, loads, heat, etc... Hard to tell anything from this because sometimes they look ugly as hell but still shoot fine. For example, I saw it starting on my last 6.5cm barrel about 800 rounds in, and it lasted til 3200 before I started getting fliers ugly enough I stopped shooting matches with it.
Good way to look at rings in the chamber from manufacturing goofs.
That all said... Very rarely is it a useful tool to look at something and say "that won't shoot because of XXX". I've seen chamber jobs so off center the rifling (or a shallow part of it anyway) went all the way back to the neck on one side of the free bore. Rifle shot fine. IMO You'll learn more from slugging a bore, and even more yet from shooting the rifle.
ETA: Carbon rings! actually a useful endeavor to find them and see if they're gone after cleaning. They'll damage bullets, spike pressure, etc...