Ethical reaction to fake academic degree claim. (Unfinished PhD)
Obligatory disclaimer: I am not a lawyer and this is not legal advice.

In Germany, using a Dr. title without having earned it is illegal, and it is punished with imprisonment up to one year or with a monetary fine (this is a link to the relevant law in German). 

The mechanism available to denounce this is to report the offending person to the police. Before doing this, I would suggest talking to a lawyer, as there might be consequences if the accusation turns out to be false. If the offending person is working as a medical doctor or some other regulated profession, the corresponding regulating association (for example, in the case of doctors, Bundesärztekammer or Medical Association of Germany) or other fair competition associations might sue the offender on the grounds of unfair competition (this has happened already several times).

The ethical thing to do depends on your particular sense of ethics. What you will do depends on what motivation you have to do it. The other person could sue you for false accusations, and going on a legal fight as a private person is very expensive, so there must be a good motivation. If the offender has been selected over you for some position and you feel that this is due to the fraudulent use of the title, you might as well just inform that particular employer of the situation. Going public is not recommended unless you have talked to a lawyer, as you could land in legal trouble if you make public accusations that turn out to be false.