Designing a voltage regulated power supply
The pots are far too high value and are connected wrong (wiper should be connected to element end on each individually). 

R1 is okay, sets resistor chain current at about 6.2mA (the chip needs a load of 5mA to regulate). 

Maximum total resistance should be (Max output voltage- 1.2V)/0.0062 so for (say) 20V maximum output, total max resistance should be about 3K. 2K + 500 ohms could be used, and then R1 dropped to increase the current for the desired maximum output voltage. Pots are not available in such a wide range of values of resistance as resistors, usually you can get 100\$\Omega\$, 200\$\Omega\$, 500\$\Omega\$, 1K\$\Omega\$, 2K\$\Omega\$, 5K\$\Omega\$, etc. 

As you have not defined input voltage, output voltage range or current, we can't really say that the capacitor values are wrong but the 1000uF smoothing capacitor is a very poor  match for a 5A regulator. You need to calculate the ripple voltage requirement and the required ripple current rating. Chances are you'll need a much higher value of capacitance, and you'll have to define the voltage rating carefully to accommodate the peaks of the waveform, and the case where the mains is a bit on the high side of nominal. For 2Vp-p ripple at 50Hz mains, your output current would be limited to less than 200mA.  

C3 could certainly be larger (or paralleled with an electrolytic capacitor) to decrease the output impedance, and C2 could be larger as well. 

R2 might be on the low side, depending on the input voltage. A modern LED requires only 1mA or so to be quite bright. 

If you are really intending on getting multiple amperes out of this, the thermal design will be important. Assuming (say) a 28V nominal input and 3V 4A output, the power dissipation would be about 100W, a non-trivial amount of heat to dispose of, requiring something of the order of a CPU cooler.