Mold can be characterized by black spots. Mold is often caused by humid conditions and lack of ventilation. Also, it is very much possible that it is being fed by a water leak somewhere inside the walls or above the ceilings. Make sure you fix that first.
You're right, exposure to mold in buildings and homes can cause serious health issues. It has also been associated with cancer. Thus, it should be taken seriously.
I at Titan Restoration deal with mold everyday. Itís important to keep in mind that killing visible mold isnít enough. A lot of DIY methods will only kill surface mold. Mold has to be remediated and a professional service is really the best option.