I think that one of the most significant improvements made to the criminal court process since the time period of the Colonists' is that due process is met with an evidential standard. So much of the legal system's proceedings in the Colonists' time period was predicated upon the notion of honor. For example, colonial "Juries were reluctant to convict a man of murder or assault if he had committed the crime to defend his honor." The notion of honor as entering into the proceedings of the legal system is something repudiated by the Fourth and Fifth Amendments of the Constitution. These amendments represent the need for a process predicated upon legal counsel, a lack of emotional subjectivity, and ensure that the legal system proceedings are fair for those who might have "honor" and even those who "lack" it. The "loose" construction of honor is replaced with a more substantive notion of due process and a sense of institutional fairness in the legal system for all individuals.
Another improvement we have made in the legal system since the time of The Declaration of Independence has been to rely on evidence as the essential portion of the legal process. In Colonial times, much of the legal surroundings was based on the presence of the divine. This rendering of the legal system as "divine social theatre" was something rejected by the secular nature of the Constitution. The legal proceedings in the Constitution provided a sense of due process that was not infused with the subjectivity of the divine. Rather, evidence in the forms of physical, eyewitness testimony, or motive- based analysis became the crux of the legal system. As the nation has grown to become more divergent and diverse, it makes sense that our legal system has embraced something rooted in more procedural and regulated issues to determine guilt as opposed to a vision of the court process where the result became an ultimatum on the presence of divine power. This is another improvement made since the Colonial times in our legal system.