I believe I have some efflorescence in my basement. It is growing in two spots where the floor paint was scratched off when the previous owners moved out. It brushes away easily, and I have never noticed any actual water in my basement. There is no staining on the concrete, or bubbling of the paint anywhere else. We had a terribly humid summer, and it only showed up late in the year when I had my dehumidifier turned off for a few weeks. Is it possible that it was caused by the moisture/humidity inside of the house as opposed to an issue with moisture entering the concrete from outside? I would like to figure out the cause so that I can correct it properly instead of just ignoring it, or wasting the time/money to replace my weeping tile if it is not necessary.
Efflorescence is caused by water or moisture permeating through concrete. When the moisture evaporates it leaves behind what ever minerals it accumulated. That is what the fluffy white residue you described is. It is easily fixed by cleaning the efflorescence with a mild acid (vinegar or citric if you prefer to keep it green) or CLR or Lime-away. Once clean concrete can be sealed with a tinted concrete latex paint (Dry-Loc) or a clear sealer that should prevent water from migrating inside.