The pot will only drop the current to a minimum, not completely off, so there could still be enough current passing to allow the led to stay lit.
Also try getting a 1 ohm resistor in series and checking the voltage across that, that will tell you the current passing through the circuit. The circuit is a current limiter (not voltage) so testing with a proper load like the diode system would be better then using an led.
My only other advice is to check the circuit and make sure it matches the diagram and check that you don't have the adjust and output pins the wrong way around.
Also try getting a 1 ohm resistor in series and checking the voltage across that, that will tell you the current passing through the circuit. The circuit is a current limiter (not voltage) so testing with a proper load like the diode system would be better then using an led.
My only other advice is to check the circuit and make sure it matches the diagram and check that you don't have the adjust and output pins the wrong way around.