In terms of legal procedure, the judges and prosecutors at the IMT went to great lengths to ensure that the trial would be ostensibly fair. Defendants were properly represented, allowed to consult with their counsel, the basic presumption of innocence applied and prosecutors required to put their case.
There was a major difference in terms of rules of evidence, whereby a greater level of documentary evidence was allowed and utilised. This was however based on the scale of what was being prosecuted and the often absence of witnesses that could be found, and to some degree a greater level of 'hearsay' than might normally be allowed in an Anglo-American court. In the case of the US prosecution, there was a preference for letting documents speak for themselves rather than using (and potentially 'exploiting" witnesses)
The consensus on the judges is that they did their job properly and well, and there weren't any issues that I can recall that might lead a judge to normally recuse themselves.
Beyond that, it becomes subjective in my opinion. Certainly accusations of tu quoque have been made - the Allies had potentially committed offences, why had they not tried their own, and especially at the presence of the Soviets. In my opinion however, I think that those involved went to great efforts to make the trials legitimate and fair - it was not in their interests for the trial to be perceived as a 'show trial' and illegitimate.
But that is my humble opinion as a mere masters candidate researching war crimes trials, and a solid B law degree.
I once researched a little presentation about the defense in Nuremberg and I found some problems with that. For example, most of the defending lawyers were german and did not know the anglo-american kind of trial the Nuremberg Trials were build after. They had worked in a completely different system of criminal law befora, so they were not very well prepared for their job. Also they had many difficulties finding defense-witnesses and bringing them tur Nuremberg for they did not posses the same infrastucture as the Allies. The same goes for many documents that werde under allied control and could not be used by the defense. Also the accusation prosecution had a huge staff while the different defense lawyers had to work with very few people under quite bad conditions. I believe that a proper defense is very imfortant to the fairness and objectiveness of a trial, even more if we talk about an anglo-american trialsystem instead of the german system.
After working and reading quite a bit about Nuremberg I believe that the trials were not perfect. There was a lack in proper defense, the tu quoque-thing was problematic, the rules and laws the trials were based on were not really established before etc. But overall I think it´s the best kind of trial that was possible a the time and under the circumstances. The world needed those trials and they were a step in the dircetions of establishing the International Criminal Law we know today. Without Nuremberg there would probably be no ICC.
EDIT: If it helps, I´m a german law-student who wrote a thesis about the ICC and had quite a few lectures and stuff about Nuremberg and International Criminal Law in general while studying in Berlin. Also sorry for the language.