Get pics of the ends of the barrels straight on, the water table, the barrel flats, the locks and any engraving, the wrists of both guns, the wood behind the locks, the butt plates, the undersides of the actions, the checkering, any imprinting on the tops of the barrels, the bottom tangs etc. Take 12ga. snap caps with you. Put a little wax over the location of the primer and and cock and fire each barrel. The wax will tell you if the firing pins are hitting the primer.
Remove the forearms of the guns, grasp the gun at the muzzles with butt hanging down and shake. If you feel something moving the gun is probably off face. Take scotch tape with you. Put a piece of tape across the standing breech centered on the firing pins and extending past the breech balls. If the barrels will close over the piece of tape the gun is off face. Check the hinge pin and hook. An easy fix for being off face is to use permanent Lock Tite to glue in a very thin piece of metal either inside the hook or over the backside of the hinge pin. On a Smith, this will usually result in the top lever moving to the right as well as putting the gun back on face.
The barrels are the heart of a SXS. Properly checking the barrels can't be done without gauges to check the barrel wall thickness, chokes and chambers. Visually you can look at the crispness of the printing on the rib and barrels. If it looks washed out they have probably been refinished. If you look at the muzzles and the barrels do not touch they have probably been cut. The next test is to "ring" the barrels. This will tell if the top and bottom ribs remain firmly soldered to the barrels. With the barrels off the action, hang the barrels, by the hook, from a finger and tap them the full length with a wooden pencil. If the fillets have started to separate you will hear distinct dead spots. Check for any dents or dings in the barrels.
Check the wood for cracks through the wrist, behind the lock plates and on the top edges of the forearm. On the Smith in particular check the horns at the top and bottom of where the wood contacts the stock. Smiths are notorious for cracking at these points.
I know this is probably too much info. but you asked.

