It´s a great advantage being obligated to report your current address to the city administration (we´re not reporting to the police). The state always knows where to write letters to you (for taxes, fines for wrong parking, notifications for elections), and it makes sure (combined with the national IS) that there´s no voter fraud, for instance. Everybody can only register in ONE city/town.
Not only when you move to a new home. Even if you spend a night in a hotel you have to fill in a so called "Meldeschein". I refused to do register for several years until a friend of mine who is working in the local town hall came with the documents into my house not letting me out. I had no chance...
;-)
Besides of this friendly pressue I am completely against the practice since I believe it is part of the individual freedom that the state is not informed about the whereabout of his common members (there must be some exceptions of course).
It is new to me that the registration happens in the police station. In Baden-Wuerttemberg where I live this is going to happen in the town halls. Maybe your horrible Oberbuergermeister in Berlin (und das ist gut so...) was so often in the police office that it is much more familiar than the town hall to him since he is meeting some gay buddys from the red-light district there. BTW - The police officers could do the gay marriages too. The drunk tank would have the right romantic ambience. Since I know many nice German policemen I am sure that they would paint it in pink for Wowereit.