The gun may be stolen and the serial on the butt was covered by large stocks and the thief missed it in his efforts to remove all numbers.
That's silly. OP, disregard that.
The serial number is on the bottom of the butt. If you want to refinish it, S&W does a really fine job for around $250. So you'll pay that, plus shipping to and from the factory. That will be ~$150.
As far as making it look good, it depends on where the numbers are that were "ground off." Are you talking about the yoke area of the gun? Or was there a number on the outside of the frame? Because if it's a number that the police department stamped into the exterior of the frame, then no amount of refinishing will fix that.
Still, if you decide to buy the gun, just make sure you get such a killer deal that you can pay the above and still have a bargain. Otherwise just go on gunbroker and buy one already fixed up.