There are a few problems with Mill's calculation of the anomalous electron magnetic moment.
1) Mills' electron theory is not based on any known formula. Mills throws out any wave equation, and simply assumes a series of superconducting loops, at the right radius.
2) He mixes and matches known formulas, including the actual results of QM, in an ad-hoc manner, not all of which is sound.
3) The g/2 = 1 + (alpha/(2 * pi)) is indeed correct, and is while it contains the first-order loop corrections in QED, it also has a classical analog. This is well known. Mills knows that, and it is no big issue that he can write it down.
4) I don't believe the next term has any type of valid derivation. I know others have pointed out that it is not the magnetic energy. I see some questionable things myself involving relativity, and no attempt to deal with Lorentz invariance.
5) Mills does not get the right answer. Sure, it is close-ish, but it is not right. In fact the signs of the next terms past what I mentioned in (3) aren't even the same, from the actual QED theoretical calculation. I bet I could hand-wave around a few changes in constants, and get an even closer result.
The truth is, Mills does not have a coherent theory. Yes, close analytical formulas are interesting, but when they don't have a rigorous basis, and aren't actually correct, you suspect that they are a result of working backwards from the solution, not working forward from a real theory.