It really is kind of hard to hurt a shotgun. Personally, I don't care how dirty the gun is. I check for mechanical problems and how smooth the action works. The older the smoother. Parts can be ordered from Brownells, so even guns with mechanical problems can be a great buy, as long as the buyer spots them and gets the price down.
Look at the barrel and see if there are any bulges. This can be from plugged barrel or shooting steel in too tight of a choke.
If the gun has choke tubes, make sure they come out easily. I have seen a couple guns that looked spotless but the choke tube was frozen by rust. This may need a soaking in Kroil or cut and re-tube.
The metal and stock finish will be reflected in the price. If its a super clean gun but only has 60% of the blueing, the price drops significantly. These are great bargains. You can spray paint them, Gunkote them, or have then reblued.
The most important thing with a shotgun is fit. If you plan to do any wing shooting, the gun needs to shoot where you look. Focus on a distant object, shut your eyes and mount the gun, when your eyes open, the barrel should be pointed at that object.