The simple answer (and someone with more legal knowledge should please chime in) is:

The unification of Germany in 1990 was legally speaking incredibly complex. To satisfy the enormous time constraints (less than six months between first draft and final signature for a treaty to unite two very different countries), the simplest solution was that West Germany would , for a split legal second, accept and recognize all of East German law at at the stroke of the pen to be able to inherit all rights and responsibilities. The Soviet Union and the Western allies had specific requirements which needed to be brought into it in a way that would satisfy all parties involved (like the future honoring of Soviet war memorials from WW II). In terms of international law it was a quite herculean effort, and it shouldn't come as a surprise that it was decided to throw a lot of babies out with the bathwater.

By accepting the legality of East Germany as a state, by the stroke of the pen all legal activities by East Germany in the past became per definition legal activity under United German law unless explicitly negotiated otherwise. Therefore (and ironically), West German state attorneys found themselves facing the absurdity that they basically could only put to trial East German officials for crimes committed against their own laws. And those proved very difficult to prove in court. East Germany had (on paper) not officially given an order to kill at the border, but the Communist Party had, and on that basis a number of trials were attempted to put border guards on trial for shooting escape attempts, but it proved nigh impossible to put those responsible for the order on trial. A lot of these proceedings did not get very far either, as the guards were often the only witnesses. Thus, to put someone like Mielke on trial, it required a crime committed that was even on paper illegal in East Germany. And hence, the only case they could properly build in time was one for the murder of a Berlin policeman in the 1920s (for murder there is no statutory lapse).

But this is only the larger picture, and the legal details might be better explained by someone with deeper knowledge on this.