YZguy, I haven't seen many recent bargains on 870s at gun shows, but one can still hope.
Here's the checklist, starting from the muzzle. AND, of course, we check the chamber and mag for safety beofre anything else.
No dings or dents in the crown. If it has a choke tube setup,ask to see the tube screwed in and out to make sure it's not rust welded in place.
Make sure it has a bead or other front sight. Lots of police turnins do not.
No dings or dents in the bbl. Minor dents can be smithed, but the price should be adjusted. Bulges are an automatic turndown.If it's a vent rib bbl, check the vents for rust.
Loosen the mag cap and check the threads on the end for dings. Retighten, then grasp the bbl in one hand and the receiver in the other and see if there's play.If so, there may be headspace probs, fixable but the price needs adjusting.
Check the mag tube for dents, and also uneven wear marks on one side. A crooked tube is also fixable, but you know the rest. Pump the action a few times, and see if it feels smooth and easy.
Look inside the ejection port and note the condition of the metal you see for rust, grunge, etc. Using a finger, feel the edge of the ejector mounted on the receiver wall,sometimes these have broken edges. A factory fix.
Check the serial number. If it ends with an "M", it can shoot 3" mags. If not, it's a 2 3/4" gun regardless of what it says on the bbl.
Look through the bbl, checking for rust, pitting, and dings. Look along the bbl to see if there'a any obvious bends.
Cycle the safety, it should move with a positive click. Also,close the action, pull the trigger with the safety on, let off the trigger and take off the safety. If you hear a click, forget this one.
Next,check the wood for cracks and so on. Look the whole thing over again for rust,etc.
Grab the pad,if so equipped, and see if it's loose. Same with the stock.
I think that about covers it, but I haven't had my coffee yet.
HTH....