All legal proceedings in the Holy Roman Empire could be brought to the Imperial Chamber Court, except if the ruler of the territory had a so-called privilegium de non appellando, in which case the highest judicial institution was found by the ruler of that territory (though the privilege could be bypassed if a litigant could claim they had been denied due process).
Another exception was criminal law in which the Imperial Chamber Court could intervene only if basic procedural rules had been violated.
[1] However, it has lately been discovered that it could often be attributed to a loss of interest on the part of the parties involved, and that the court was sometimes much more efficient than previously thought.
Recent research has also brought to light that especially in the 18th century, the rulings of the court anticipated in many ways the constitutional establishment of civil liberties in Germany.
The creation of a new and efficient court became a matter of pressing necessity, and it was one of the most urgent of the reforms which were mooted in the reign of Maximilian I.
[1] The "province of the Imperial Chamber", as it came to be gradually defined by statute and use, extended to breaches of the public peace, cases of arbitrary distraint (property seizure) or imprisonment, pleas which concerned the treasury, violations of the Emperor's decrees or the laws passed by the Imperial Diet, disputes about property between immediate tenants of the Empire or the subjects of different rulers, and finally suits against immediate tenants of the Empire, with the exception of criminal charges and matters relating to imperial fiefs, which went to the Aulic Council.
The competition between the Aulic Council and the Imperial Chamber was finally regulated by the Peace of Westphalia in 1648, which laid down that the court which first dealt with a case should alone have competence to pursue it.
The court did take payments from parties hoping to make their case a priority, but these were not expected and it didn't seem they affected the objectivity of the judges.
[3] The Peace of Westphalia in 1648 ruled that half of the members of the court must be Protestant, and called for a total of 50 judges to be appointed at any time.