I would argue that the main barrier to fair trials in the United States is the cost of lawyers. A person who can afford a good lawyer is likely to get a fair trial. A person who must rely on a public defender is much less likely to get a fair trial.
This is a different idea than that put forward by the previous answer. An answer that doesn't talk about people who had trials and were acquitted, like readerofbooks' answer, but instead talks about people who were never brought to trial, may show that our laws are unfair, but that says nothing about trials.
Our system of trials is generally fair. However, it is only truly fair to those who can hire good lawyers. Public defenders tend to be badly overworked. This leads to a situation in which they are often unable to defend their clients as aggressively as good lawyers would defend paying clients.
Because our system is so complicated, it is hard for it to be completely fair because the people who can hire the best lawyers will typically have better outcomes than those who cannot.
Answer #1 submitted by readerofbooks is an excellent example of how not to think about the law. While there is no question that a correlation exists between quality -- and, consequently, cost -- of one's attorney and the probability of an acquittal, the assumption of innocence until proven guilty is the main cornerstone of this country's criminal justice system. With regard to the conduct of those individuals "responsible" for the economic crisis, it is first a good idea to determine whether laws were in fact violated. An assumption of criminality, and demand for punishment, when no guilt has been proven in a court of law, is the difference between freedom and tyranny. Hopefully, those teaching the youth of America recognize that distinction.
It is probably best to start off by saying that no system of law is perfect. We live in an imperfect world and so all systems are fallible. With that said, the principle that the United States goes by is very noble - a person is innocent, unless he or she is proven guilty. This starting point puts the burden of proof on the accuser.
The one area where I think we do not have a fair trial is when it comes to people with wealth and power. Usually, the law is much more lenient. For example, very few people went to jail in view of the financial debacle in 2008. We should make no mistake that many of these people were criminals, who hurt many people. In light of this, we seem to have a two-tiered system. The wealth get preferential treatment.