"What Do You Look For That Says This Is a Well Made Gun?"
In reference to doubles I first look for my shooting student and double gun mentor, Joe Wood, and ask him.
When he isn't sober enough to talk then I look for metal to metal fit on the floor plate and, if a sidelock, how well the lockplates fit into the action. I look for timed screws and how well they fit the surrounding metal.
I also look at the wood to metal fit, the quality of the engraving, and the quantity of the engraving. I look at the quality and quantity of checkering. I look for overruns in the checkering. Is the checkering flat topped? I look for borders around the checkeriing. I look for the corners of the outside of the pattern to be cut accurately with no overruns or undershoots. Joe taught me to look at the engraving and finish of the fin on the thumblever.
I look at the fit and finish at the muzzles. I look for keels in the muzzle. I look at the finish of the water table and the barrel flats. I look at the quality of the engraving on the rib and on the barrel flats.
I look to see where and when it was made. If it was made in England between WWI and WWII then I just assume it is was quality built. If it says Parker, Fox/Philadelphia, or Ithaca I assume it is built well. Haven't gotten around to the owning the Elsie's yet. If it says Beretta or Winchester I assume it to be well made.
With the gun closed, I look at the gap between the water table and the barrel flats towards the butt end of the gun.
Edit: If it was made in Germany before WWII I assume it to be well made.