Why is my MOSFET switch circut not working?
simulate this circuit &ndash; Schematic created using CircuitLab

Try the above. Your circuit has two problems, first it is not giving the MOSFET the full 6V on the gate (relative to source), rather it is reduced by the LED forward drop. That is solved by putting the LED in the drain circuit. 

Second is that there is no way to discharge the gate charge on the MOSFET so it will tend to retain the previous on or off state for some time when the switch is open, until leakage causes it to go towards 'on' or 'off'.