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 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 . The measured value differs from 2 by a little bit, a fact well accounted for in QED.
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Some of the errors in the theory are related to our knowledge of constants such as , 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.