Next, inspect the frame and slide. Make sure that the rails aren't cracked, dinged, or otherwise damaged. The slide should travel smoothly on the frame without binding, and check for peening of the slide and frame. Peening is usually caused by a weak recoil spring, loads of shooting or shooting hot +P rounds, poor maintenance, or any combination of the above. Be wary of a pistol with this kind of damage, even if it's just a beater.
OK, time to move on to the barrel. From my experience selling used guns, it seems the first thing most folks want to do is press down on the hood of the barrel. In the days of old 1911s this was a good test to see if the barrel link/pin fit well. But on most modern firearms this will serve little or no purpose; nor will trying to wiggle the muzzle of the barrel in the slide. If you work it hard enough the barrel will move. The barrel has to have some play to function properly.
After checking for barrel fit, remove the barrel. You are checking the locking lugs of the barrel and the throat of the barrel. Look down the barrel to see what shape the lands and grooves are in. Unless this is a polygonal barrel like a Glock, they will be barely pronounced. You also want to feel down the barrel to make sure there are no bulges; bulges are a sign that the pistol was shot with an obstruction. If you feel one, move on. A bulge in the barrel is very bad; it's potentially deadly should you decide to shoot the gun.
While the barrel is out of the slide, check the slide's interior. Look at the firing pin area. If it is smooth and concentric, this means the firing pin functions properly. If the firing pin area is nasty looking and not dirty, it could be that the owner was running hot home reloads and there was primer flow. This could lead to other unseen issues with the pistol. Pass it up.
One other thing you want to check while the pistol is disassembled is the inside of the frame. You want it to be in good shape with no cracks. Most of the time you will see very little wear on the inside of the frame; maybe some scratches from dirt, but that's about it. The feed ramp should not be dinged up, as it shouldn't get damaged from normal use. The finish on the feed ramp may wear off, but it shouldn't be chipped.