What is the purpose of a resistor in series with a potentiometer?
In this case the resistor is only needed if a minimum resistance is desired to eg. set a minimum output voltage or simulate a maximum load. The 1k resistor in the shunt regulator should prevent too much current from flowing even if the pot is set to zero Ohms. 

However in many circuits the pot might short out other parts of the circuit, causing excessively high current or overloading a signal output. It is also a good idea to add a resistor in experimental circuits where the pot might might be wired incorrectly. For example if you connect it across the power supply rails as voltage divider but have the center and outside terminals crossed over, the pot track may burn up when turned to minimum resistance at that end.