It is hard to say that a theory has predictive power without comparing it to experiment, so let me highlight a few successes of QED.
One of those is the so-called $g$ factor of the electron, related to the ratio of the spin and orbital contributions to the magnetic moment. Relativistic theory (i.e., the Dirac equation) shows that $g=2$. The measured value diﬀers from 2 by a little bit, a fact well accounted for in QED.
$$\begin{array}{cc}experiment\hfill & g\u22152=1.00115965241\left(20\right)\hfill \\ Theory\hfill & g\u22152=1.00115965238\left(26\right)\hfill \\ \hfill \end{array}$$ | (6.19) |
Some of the errors in the theory are related to our knowledge of constants such as $\hslash $, and require better input. It is also clear that at some scale QCD (the theory of strong interactions) will start playing a rôle. We are approaching that limit.