OK, my thoughts:
1.) You already have jacks for +12V and 1.25-9V. Why give up one to have the other? If you are 5A capable, most bread boarding doesn't require that much current from all of the supplies combined. So you could run your +12 to the jack and an LM350T circuit, and just watch your combined output. Just change your variable output fuse to a 5A too.
2.) You didn't label your current setting resistor. If it's 240 ohms, you would be wasting most of your pot. A 390 ohm resistor would cause the supply to max out at around 9.25V.
3.)Keep the bodies of the resistors as close to the adjustment pin as possible since that is a very high impedance input. Twist leads going to the pot. If you add the 10uF cap for better ripple rejection, also add the extra diode across the 390 ohm resistor, cathode up. 1N4001, 1N914, 1N4148A would all be fine.
4.) The best place to learn how a chip works is usually straight from the mfg.
http://www.onsemi.com/pub_link/Collateral/LM350-D.PDF
OnSemi seems to have about the most complete datasheet for the LM350 these days. Page 2 is telling us that the reference voltage is typically 1.25V, adj. current 50uA, that I need to have around a 3.5mA load to regulate, and that I might be able to get 4.5A out of it. Page 5 shows how you can get more than 3A out of it(Fig.8), and how much more input voltage you need for different currents.(Fig.10) Figures 13 and 14 on Page 6, show how the 10uF helps. Pages 7 and 8 show useful applications.
Joe