So, I have built that power supply
Which version? The original, a modified one or the latest modification?
Which transformer? 24VAC, 28VAC or 30VAC?
Which opamps? TL081, MC34071 or TLE2141?
P1 (voltage control pot) - without a load on the output i've got 7mV to 5V
The output should be able to go from calibrated 0V to calibrated 30.0V.
Measure the output voltage of U1. It should be about 11.2V. The output amplifier has a calibrated gain of 2.68 times to make the output 30.0V max.
at maximum voltage pot position, current limiting turns on (while P2 is on the maximum, while less, current limiting is constantly turned on and output voltage is about -200mV).
Your current regulator U3 is not working correctly. Its output should be high (so that D9 cannot reduce the output voltage and does not turn on the LED) until the load current in R7 causes as voltage drop that is more than the amount of voltage set by P2.
U1 gets too hot in my opinion - after 10 minutes of test run it was about 80-90 celsius degrees.
If you used DIP 14 pins case opamps then their maximum allowed dissipation is 1000mW when the anbient is 25 degrees C.
The MC34071 will dissipate a maximum of 302mW and the TLE2141 will dissipate a max of 470mW. Not too hot.