I have to express some divided feelings. I have polished and reblued many guns that were in such poor condition that they had essentially no value. I like to think that when I was done the gun looked much better and had at least a shooter value.
There are a lot of tricks to rebluing.
First, I am not talking about a full, expensive restoration. Full restoration by someone like Turnbull is justified only when the gun is of such rarity and in such condition that its value can only be enhanced even with the fact of its restoration known and acknowledged. Restoration for the purpose of fraud, to pass the gun off as original at the price of an original, is a crime, literally and figuratively.
But a so-so gun, well worn and/or with rust, can often be improved by a good reblue job. The most critical item is the polishing, of which some mention has been made. In polishing, the most common mistake is to polish too much. The old time gunsmith books urged imparting a "mirror finish" in polishing, using the finest grit compounds available. Some people do like that finish, and companies like Weatherby have used it.
But in most cases, if the gun is to look anywhere near original, a high polish won't do. Factories simply do not polish that well. Far from a 1000 or finer grit equivalent, most factories used closer to 600 or even 300 grit. Some, in wartime, would get the equivalent of 60-80 grit, just enough to clean up tool burrs. Anyone doubting this can use blue remover instead of an abrasive wheel and look at the surface under the blue for the factory finish.
With the proper polishing, various types of bluing can be simulated in the hot tank. A coarser grit can emulate rust blue, for example. The key is light refraction, where a finish can appear blue, or black or brown depending on the light. In a dark room, turn a Maglite on your prized 1900-era Luger and you will scream as it looks like it is covered with brown rust. That is the way rust blue reacts to that type of light.
A buffing wheel used improperly can easily round corners, blur markings and "dish" pin and screw holes, so at times draw filing or polishing the gun on a glass plate covered with emery cloth is a good approach. Factories use hard wheels, specially shaped to the part being polished, so those problem are reduced or eliminated. (Yes, factories sometimes turn out dished holes, but it is not common.)
Sorry, folks, but this is getting too long and I have some other stuff to do.