There are very few governments in countries with settled democratic systems which it is possible to imagine running something comparable to Guantanamo Bay. Maybe places like Uzbekistan, Saudi Arabis, Belarus, and true enough, if Bin Laden was running a country...

Given the number of cases where it has turned out that people who have been imprisoned for years, sometimes on Death Row, were completely innocent, can anyone say they really "trust" the US justice system?

At best with any justice system, it has to be a cross-your-fingers-and-hope for-the-best kind of trust, combined with trying to find ways of making it better, and cobbling up some kind of correction for mistakes that have ruined people's lives.