Power supply circuit concerns
About the resistors R3 and R6, is it correct to pull up a MOSFET gate for such operations? Should I pull it down instead? Or remove the resistors? I am concerned about LM324 output sink/source capabilities with those resistors.


R3 and R6 have no effect, except maybe during startup. I would make R6 a pulldown to help start the output at 0V.


  Also, in my output circuit, should I add other components to improve safety and stability? 


As drawn, the current control is probably unstable because it has gain but no compensation. Add a resistor (10k?) between the shunt and the inverting input, and a small capacitor (100p?) between the output and inverting input of U1B. This slows down the current control by making fast changes to its output appear immediately at its inverting output and will prevent it from oscillating.

Also, the output resistance will be 1 ohm, because the voltage control doesn't consider R4. Overall I don't think this is a good setup. You should look at some other bench power supply schematics and see what they do.