Of course, we can. To right there is wrongs (and thus to ensure that the genuine justice is done), it is necessary to first acknowledge the cold hard legal truth – that the main Nuremberg Trial violated the most basic principles of criminal justice and thus was legally invalid (null and void).
To do that, the United Nations must establish a one-time Special Appeals Tribunal specifically for the purpose of righting the wrongs (the miscarriages of justice) committed by the main Nuremberg Trial. Which will overturn all verdicts of the Nuremberg Trial and declare all defendants not guilty de-jure.
However, because of the gravity of crimes committed, the Tribunal will explicitly rule that the double jeopardy principle does not apply to defendants. In other words, effectively declare a mistrial.
Which means that the defendants must be retried (obviously, in absentia). Consequently, the Tribunal will set a date for a new (and a very public) trial, which will be conducted according to the highest legal standards (i.e. the way it should have happened in 1945).
However, unlike in 1945, this Tribunal will investigate all war crimes and crimes against humanity committed by all belligerent nations and thus will investigate, persecute, indict and try both German and Allied war criminals.
To ensure the maximum possible impartiality of the trial, it will be held not in Nuremberg (obviously), but in the only appropriate major city – Stockholm. And thus will be known as the Stockholm Trial.
The Tribunal will set up Office of Investigations and Office of the Prosecution – staffed, obviously, with fair and impartial investigators and prosecutors from nations that were neutral during World War II – Spain, Portugal, Ireland, Sweden and Switzerland.
Given the fact, that Germans have been subjected to an omnipresent anti-Nazi propaganda, the defense team will also be selected from the neutral nations. For the maximum impartiality, the presiding judge will be selected (with the approval of both prosecution and the defense) from a list of prominent and impartial Swedish criminal judges.
Given the fact that the gravity of crimes committed warranted capital punishment, the defendants will be tried by the jury – twelve jurors from the neutral countries. Selected by both prosecution and defense.
This time, there will be only one official language of the court – English. Given the fact that most relevant documents will be originally in German, all investigators, prosecutors, defense counsels, judge and jury must be fluent in German and English.
As all defendants will be tried in absentia, no plea bargain on behalf of the defendants will be allowed. However, the prosecution will be allowed to drop the charges against the defendants by making an official statement to the court in which it will explain why there is no evidence that would support the indictment of the defendant in question. Which will drastically reduce the number of defendants in court.
Because defendants will be tried in absentia, the list of defendants will include Adolf Hitler and other leaders of the Third Reich who were not tried at all or were tried in absentia – Martin Bormann, Heinrich Himmler, Joseph Goebbels, Reinhard Heydrich and Robert Ley.
It will also include leaders and officials of Allied nations (the Soviet Union, Great Britain, the USA, etc.) charged with war crimes and crimes against humanity.
Prosecution and defense will be given considerable time – a year – to prepare their cases, after which the trial will begin. And, given the fact that the gravity of the crime warrants capital punishment, the Tribunal will establish the Appeals Board to which guilty verdicts (and death sentences) can be appealed. This Board will pronounce the final verdicts – whatever they happen to be.