When you don't have the gun in hand, you have to ask questions and hope the seller is more honest than someone I could name.
Ask about exterior finish (I agree with Willy that it does indicate a degree of care) but also about where it came from. Most police guns see little firing and lots of carry wear. Guns used by some folks on this site would certainly be the reverse. Ask if gun is reblued or refinished. If so, best forget it, mainly because you don't know what it looked like before it was refinished. (There are exceptions: I'll take a genuine Colt Paterson for $100 even if it has been reblued.) Ask if it works OK, is loose, has had work done on it.
If you have the gun, following things to check:
Auto pistol:
Safety(ies) don't work, slide loose, barrel loose, trigger pull too light, screws buggered, pins loose, hammer drops when slide is dropped, hammer has no half-cock and is supposed to, mag release is too stiff or too easy, gun has a lot of "custom" features that might not work, barrel not rusted, worn out or bulged. Main question is if this is as good a gun as seller says it is, how come seller (or previous owner) wants to get rid of it?
Revolver:
Cylinder end shake, cylinder "wiggle" when cocked (some is normal in S&W and other revolvers), full cylinder lockup when fired normally (old Colt DAs won't when cocked slowly, but work OK when fired), hammer stays cocked can't be pushed off full cock,
DA pull is reasonable, safety block/transfer bar in place, barrel cylinder gap not too much or too little, no rust in barrel, barrel not worn out or bulged.
Obviously, knowing what to look at requires experience. Look at as many guns of the type you are interested in as possible, and get an idea of what is "normal". Some things are judgement calls, like a .45 M1911A1 with a shot out barrel. Barrels are easy to get and replace. If the gun other wise is OK, and price is right, maybe buy. But an S&W .44 Magnum with a shot out barrel had better be real cheap; barrel replacement will cost bucks.