If the barrel walls are thick enough ream it and polish it.
I've reamed a couple using a step reamer I found cheap at a salvage store. It has a shank I can turn using a socket wrench with extensions.
You can ream a 12 gauge a couple of hundreths oversize without adversely affecting function, even with old style card wads. The modern plastic shot cups seal even better than wadding ever did.
Some like to back bore new barrels so its not an uncommon procedure. This is also handy for restoring choke to a cut down barrel.
Serial numbers were not required on shotguns (or .22 rifles) by law till the 50's. Most manufacturers used serial numbers soley to keep track of the gun during manufacture to regulate quality control.
Others used the numbers to keep track of which wholesaler or retailer got what.
I've heard of dealers stamping their own numbers on some old guns and registering them with the BATF, but I don't think its necessary for an owner to do so.