First thing is first. Because the 555 timer has a fixed on/off time (set by the 4.7k, 15k and 10nF cap) the value of your inductor is critical. When the mosfet is 'on' the current through the inductor ramps up until its core is saturated - at which time it can't put any more energy into making a magnetic field, so it effectively jsut becomes 'a piece of wire' - one with low ressitance. If you were to leave the mosfet on, it is switching the +12V fom your supply, to ground via a very low resistance. Depending on how much current your power supply can deliver, this can be many amps, which would cause your FET to get extremely hot.
Also, the 'off time'. During this phase the inductor dumps its energy into the main cap via the diode. The voltage at the diode is set by the capacitors voltage (which increases as its charged). Eventually the inductor runs out of juice so that phase is complete. If the 'of-time' is too short however, the inductor's current won't have time to reach zero, so then ext 'on time' will cause it to reach its saturation point quicker....etc.etc...
So, I would remove the inductor, mosfet, and diode, and check that the 555 is actually oscillating. (maybe bad connection, wiring etc..). Once that checks out you should check the ressitor values on the 555 (between pins 6 and 7, an also the resistor between 7, and 8) so that the 'on-time' is very short, bu the 'off time' is very long. You can use various online applets to caculate the values for on, and off times
. Then, using your inductor value (can you measure this?) you can work out how long it will take for the current to reach a certain limit - say, 1A. Inductors have a maximum saturation curent which you want to stay under.
Thats probably and overly complicated explaination, but this kind of circuit really does require specific part values for the inductor used, to help efficiency, but also to actually 'make it work'. I see no problem with the comparator part, it should turn of the 555 (and therefore the MOSFET) when the cap has reached its set voltage - but the led will most likely just go 'dim' as the capcitor discharges through the resistors, so it goes below the thrshold, turning the 555 on again - just long enough fpr the capacitor to reach the threshold voltage once again. So in that state, the whole system is quickly turning on and off as the capcitors voltage sits bang on the set voltage.
I've made a few such cap chargers, and when they work, they work well, but without a scope (I've only just got one...) it can be quite dificult to get things to run without over heating.