The limitations would be how much evidence was available and the truthfulness of the witnesses. The Code dealt with violations of the law. The law specified punishments based on who you were...slave or master, etc..
The Hammurabi Code provided precise guidelines to maintain social order of the society in Antique Baylonia. This code was based on the law of retaliation (Eye for an eye), but also provided elelements of which later would be known as presumption of innocence. This presumption served as basis to provide trials as fair as possible, however, these trials were limited by the reliability of the evidence back in the time. Also, the trials were limited to the possible bias influenced by social position and other variables.