Stability of Constant Current circuit
This solved all of our problems, but we want to know why


The phase margin of the op-amp is 50 degrees. In other words it's 50 degrees away from becoming an oscillator at unity gain (1.4 MHz). The MOSFET has a gate capacitance of about 4 nF but it's operating in a unity gain configuration i.e. a source follower. In perfect circumstances this will prevent the gate source capacitance from loading the op-amp.

However, with such a small source resistor, it'll probably be running at a voltage gain of maybe 0.7 (gate to source). This means you will see a capacitance from gate to 0V of about 30% of 4 nF i.e. 1.2 nF.

1.2 nF and 150 ohm (gate resistor) form a low pass filter with 3 dB point at about 880 kHz (and produces a phase shift of 45 degrees). This is degrading the phase margin and, somewhere just below the unity gain frequency of the op-amp, phase margin will be degraded to the point that the circuit becomes an oscillator.

With the extra RC added (R4 and C1), you have made the circuit stable because the op-amp will effectively "become" unity gain at 159 Hz. This is fine for stability but not so good if you wish to dynamically move the constant current around quickly.

You could also have just lowered the 150 ohm to possibly less than one-third its value but of course care has to be exercised that the capacitor loading the op-amp (gate capacitance) doesn't cause ringing on the op-amp output.