I recommend that the label contain locality information in as much detail as you can provide: for mines, this includes the level, stope, cross-cut, etc.; the GPS coordinates, if you have them; address, city, township, county, state, etc. If you have not collected the specimen, all this information may not be available; the currently desired minimum information is the county (or equivalent), state (or equivalent), and country (or equivalent).
What about existing labels? I generally make my own label as well (you may want to save the old label in a separate place if it is delicate). Some locality information may be out of date (e.g., "Czechoslovakia" or "USSR").
For localities, don't add new information that did not come with the specimen, unless you can indicate on the label that you are doing so. One way is to put the new information in brackets, ideally with your initials labeling the change:
[Czech Republic]mjc, formerly Czechoslovakia