Thanks, Hippynerd! You've helped me a lot lately

When my final 8x8x8 LED cube will be done, I will symbolically dedicate one of it's LEDs to you

Another one is definitely for CrossRoads and the rest of you guys who have given me so many useful bits of information should also get one

I guess I'm talking nonsense here, but hey, it's my way of expressing gratitude.
So back to the hardware, I agree with you. The gate-source resistors are needed as pull-up resistors (I've just learnt today what that means). The resistors between the shift register and the mosfets can probably be left out, as CrossRoads said earlier.
As for the LED cathode resistors, I think the safe way to go is to calculate their value based on a voltage of 5V - 3.3V (5V comes from the power supply and 3.3V is the voltage drop across the LED). With a target current of 20 mA, we get 100 Ohms for the resistor value (
http://led.linear1.org/1led.wiz?VS=5;VF=3.3;ID=20). Even if the mosfet drops an additional 0.5V (which I don't know, I'm just assuming the worst here), with 100 Ohm resistors the current passing through the LEDs will be about 13 mA, which should be well enough for the LEDs to work properly.
I've done some experiments a few months back with some standard 5 mm white and blue LEDs and they give up pretty strong light even at 0.5 mA. I don't know if that's still true when they are switched very fast. I don't know if their turn-on time is affected by the intensity of the current. I guess we'll find out

Anyway, for the 4x4x4 test cube I will include some variable resistors in line with the 100 Ohm resistors to see how much I can reduce the current without affecting the cube's light levels too much. This way, wehn I build the real cube, the 8x8x8 one, I might be able to use resistors which will reduce the current values much and this way the cube's power requirements will be significantly lower.