LM317 voltage regulator short circuit
My LM317 potentiometer burned down with pretty bad smoke. ... I was wondering whether could this happen because of shorting the output of the LM317.


No, for shorting output to ground.
Yes for shorting LM317 input to output.

If you short the LM317 input to output you will apply 28V across R1 and R2 in series. You get the maximum power in R2 when R1 = R2 = 240 Ohms. At that point P(R1+R2) = V^2/R = 28^2/480 = 1.6 Watts.
Dissipation in R2 = 0.8 Watts
Voltage across R2 = 14 Volts.

If R2 is a low wattage rated pot (much less than 1 Watt) this could destroy it.

Usually when R1=R2 the LM317 acts to place 1.25V across R1 and 1.25V across R2 and dissipation in the resistors is much lower. Shorting the LM317 removes the protection that it usually provides.



Any action which stops the LM317 acting to control output voltage and which allows higher voltages to appear across the pot or part of it may cause such problems.