Lab power supply CC with comparator: principle
I built something like this recently and I can offer my opinions.  But, I'm not an expert by any means so if I get something wrong maybe a more seasoned reviewer can correct me.

It would seem like the current control comparator would oscillate wildly as you say, but notice how the author has included hysteresis (positive feedback) through R9.  This creates two different reference voltages depending on whether the output is high or low.  The input voltage (taken from the current sense resistors R26 and R27) can "wiggle" between these two reference points without causing the comparator to flip states.  In effect, the hysteresis (look it up there are plenty of very good sources on this subject) reduces the sensitivity of the comparator and reduces the wild back and forth servo like action on IC2.

Since the comparator has an open collector output, it needs a pull-up resistor to define a high state.  This is provided by R8.  The orientation of D7 is explained by the fact that the comparator can only sink current.  

So, summing all this up, The current control comparator acts on IC2 (the main voltage control comparator) to cause it to adjust the output voltage.  This output voltage will deliver the required current to the load that makes the voltage developed at the current sense resistors equal to (allowing for the hysteresis) the reference voltage on IC1.

At least I think that's what is happening!:-) Incidentally, this circuit is quite a classic design and whilst the supply I built used a somewhat different design, it was very similar and (in the end) worked very well.  If you have any more questions feel free to ask.