RFG, let me post some pictures of a couple original 32 Safeties. Look at the details, sideplate seams should be almost invisible, trigger and trigger guard almost never plated, sharp edges on all metal surfaces, and stampings crisp. If you compare to yours, you might see what we are discussing. This might help you assess any future purchases.
Members have already detailed some non-original features of your revolver and I can review them so it gives you something to compare. The Safety revolver always had a half-moon front sight (forged or pinned), the front of the rib is slightly set back, but square cut in the front, the trigger and trigger guard are blued or case colored, stocks should be black hard rubber with the S&W logo at the top of the stocks, pins from the factory are always extended above the metal surfaces, and stampings are either slightly raised around the edges or very sharp without dishing. All screw holes and pin holes are flat and no dishing should be seen. Lastly, the finish should look like nickel and not chrome. All vintage S&W Safeties were blued or nickel plated. Short barreled 32 Safeties will either have the address and patent dates stamped on the right side of the barrel or none stamped anywhere, since there was not enough room on the rib to insert all the information.
We have all been where you are with not knowing exactly what to look for, but buying these guns can become an addiction. The more one can learn about what to look for, the better your purchases will be in the future.