Many people have asked how one can get rid of white spots. These decalcifications usually occurs after one has gone through ortho treatment, although hypocalcification can occur after bleaching (white spots appear frosty white).
There are two methods a dentist may use to help git rid of the white spots.
#1: Bleach the teeth even more
As you lighten the remaining tooth structure, the contrast fades. The white spot(s) may appear to fade away. Power bleaching increases permeability of enamel (similar to the way it was when the patient was 14 years old), and will then allow the surrounding tooth structure to get REALLY white. You can't get whiter than WHITE. So the surrouding tooth structure tends to almost catch up in color to the spots. End result is that the spots are still there, but they will blend much better.
If the bleaching does not remove the white decalcified spot enough to your expectations, the dentist can use a course diamond and remove the spot mechanically with a strong bevel all the way around the spot. This can be done without any anesthesia. A translucent composite is then placed over it.