The first and most obvious one is that the trials were not going to based on the laws of one country and they all had to agree on how to move forward and conduct the trials in a more fair way to both sides, that is to let the losing side defend themselves for their action, which is what they United States of America initially wanted. This was still a problem because this is the first that such an event had occurred and this is was when the concept of International Law had come from for the countries to properly persecute the Nazi officials.
In 1945, the Allied powers had a convention in London, England, where they had come up and agreed on the legal laws and procedures for the trials. The charter is known as London Charter of the International Military Tribunal. With other things in it, the Charter described three types of crimes that were to be issued against the Nazi's; the crimes included both the civilian officials and the military official. The civilian officials, as earlier stated, include persons like doctors, bank investors etc. The three types of crimes that were defined were as follows; crimes against humanity, this included murder, persecution based on either religious, racial or political discrimination; crimes against peace, this included starting or waging wars in violation of international agreements; and the 3rd type was war crime and this included violations of laws of war.
The Allied Powers had chosen Nuremberg because it then was the least affected by the war and also because of the significant symbolic reason that it posed, being that this was annual site for Nazi propaganda rallies and it symbolically showed that the Nazi regime was finally destroyed and a new type of government was going to replace it.
The Nuremberg Trials were divided into several smaller trials. The most famous being held from 1945 until 1946. This was a trial about the war criminals, most precisely the major war criminals, who were the main officials in the Nazi government.