Hi Phaethom,
1) The voltage of C1 is low because a 24VAC transformer is 25VAC without a load and its peak is 35.4V. the rectifiers drop it to about only 34VDC.
2) Pin 4 of U2 has a 5.6V zener diode. Maybe you used one that is made for a high current, so its voltage is low in this circuit.
3) Pin 6 of U1 should be 11.2V but maybe you used a zener diode made for a high current so its voltage is low in this circuit.
Even with your low voltages, the output amplifier has a gain of 3.07 so your max output voltage should be near +30.7V, not just +19.98V. R11 and R12 determine the gain of the output amplifier. Check their values.
What is the part number of the 5.6V zener diodes that you used?
Without a load and with the voltage pot and the current pot turned to max, is the current-regulating LED turned on? What is the output voltage? What is the voltage at pin 6 of U2?