The branches of government are limited by procedural due process in the following ways. First, the judiciary will strike down Congressional laws which violate the Constitution. If a law is passed which deprives a fundamental right without a sufficient justification, Congress knows that the law will be struck down. So, they are less likely to pass laws which approach a Constitutional violation.
Second, the Judiciary is limited by the due process clause because they have interpreted it to protect only those rights which are deeply rooted and "fundamental." If someone asserts that a government action deprived them of a right which the court does not recognize as fundamental, they cannot, following stare decisis, strike it down.
Third, the Executive is limited in terms of agencies that set policy. Executive agencies (DOT, DOE, ONDCP, etc) set national policy in their specific areas, and those policies are subject to the same restrictions as Congressional laws--they must comport with the due process clause.
Essentially, the due process clause keeps lawmakers and policy-makers from over-stepping their authority, and keeps the judiciary from unreasonably limiting the other branches' ability to govern.
