I suspect that he misinterprets, as it were, what an interpretation is, namely, a way of thinking that elucidates the underlying mathematical framework. He seems to think that different interpretations can make different predictions based on the same math:
We are led by the Copenhagen Interpretation to expect that the positions of the interference minima should have no particular significance, and that the wires should intercept 6% of the light they do for uniform illumination.
...
Thus, it appears that both the Copenhagen Interpretation and the Many-Worlds Interpretation have been falsified by experiment.
Does this mean that the theory of quantum mechanics has also been falsified? No indeed! The quantum formalism has no problem in predicting the Afshar result. A simple quantum mechanical calculation using the standard formalism shows that the wires should intercept only a very small fraction of the light. The problem encountered by the Copenhagen and Many-Worlds Interpretations is that the Afshar Experiment has identified a situation in which these popular interpretations of quantum mechanics are inconsistent with the quantum formalism itself.
I would say that, more likely than not, his mental model of what an interpretation is is different from what physicists tend to mean. It does not help that he has an ax to grind, as the author of his pet "transactional" interpretation.
Reread this statement, which you quoted: "The problem encountered by the Copenhagen and Many-Worlds Interpretations is that the Afshar Experiment has identified a situation in which these popular interpretations of quantum mechanics are inconsistent with the quantum formalism itself."
The implication is that Copenhagen and Many-Worlds are not valid interpretations, since (he claims) they are inconsistent with the formalism. (I'm not sufficiently well-versed in QM to evaluate this claim, unfortunately.)
Suppose we had a model M that we thought described cannons and cannon balls. M consists of a set of mathematical assertions about cannons, and the hypothesis is that these fully describe cannons in the sense that any question about cannons ("what trajectory do cannon balls follow for certain firing angles?", "Which angle should we pick to hit a certain target?") can be answered by deriving statements from M. Suppose further that M is specified in a certain mathematical system called A, consisting of axioms A1...An.
Now there is much to be said about good ways to find out whether M is true of cannons or not, but consider just this particular (strange) outcome: Suppose we discover that a crucial question about cannons - e.g. Q="Do cannon balls always land on the ground, for all firing angles?" - turned out to be not just un-answerable by our model M but formally independent of the mathematical system A in the sense that the addition of some axiom A0 implies Q, while the addition of its negation, ~A0, implies ~Q.
What would this say about our model for cannons? Let's suppose that we can take Q as a prima facie substantive question with a definitive yes or no answer regardless of any model or axiomatization. At the very least it seems that M must be an incomplete model of cannons if the system in which it is specified is insufficient to answer the various questions of interest. It seems to me that
If a question about reality turns out to be logically independent of a model M, then M is not a complete model of reality.
Now we have an axiomatization of mathematics -- let's say it's ZFC for now -- and we have a model of computation in reality, which is M="The unvierse can contain machines that (efficiently) compute F iff there exists a Turing machine that (efficiently) computes F" with appropriate definitions of what exactly a Turing machine is in terms of ZFC. Suppose we want to answer a question like Q="Can the universe contain machines that efficiently solve SAT?"
Under the premise that M is true, the question Q becomes the pure logical question R="Are there Turing machines that efficiently solve SAT?", i.e. the P versus NP problem.
Now suppose that R was shown to be formally independent of ZFC in the sense that for some axiom A0, ZFC+A0 implies P=NP and ZFC+~A implies P!=NP. This would resolve the mathematical question of P versus NP but the question Q seems like a prima facie concrete question with a definitive yes or no answer that does not rely for its substance on M or ZFC or any other epistemic construct. It would seem that we must have missed something in our description of reality, M.
Perhaps more controversially, I claim: Under the correct model M' it seems that it's impossible for a substantive question (such as Q) to be unanswerable.
All this adds up to: The P versus NP problem (and questions like it that can be phrased as definitive questions about reality) must have an answer unless our model of reality is incomplete.