scerir quotes Basil Hiley saying:
Sure there is an interference effect simply because Afshar's experiments do not 'follow' anything and they do not 'look at' each photon as it passes through a pinhole. He is simply collecting and counting the distribution of photon arrivals at his two detectors. Then he makes inferences about what could possibly be going on and concludes, incorrectly that a photon detected in the 'photon detector for pinhole 1' came from pinhole 1. However that conclusion is based on the assumption that the rays emanating from pinhole 1 arrive at the 'photon detector for pinhole 1'. But the ray picture breaks down as soon as you enter the region of overlap of the two beams and you cannot conclude that the photon entering pinhole 1 arrives at the 'photon detector for pinhole 1'. You haven't measured which pinhole each photon passed through so you have not contradicted Bohr.
Unfortunately Afshar's conclusion, "According to my experiment one of the key assumptions about quantum theory is wrong" is incorrect. His conclusion is wrong simply because he doesn't understand the physical optics that lies behind the experiment he is doing.
I think Basil Hiley's analysis here may be incorrect. In the normal double-slit experiment, the interference pattern in probabilities you get from quantum physics when you don't know which slit the photon went through is the same as the interference pattern in light intensities you get from classical optics when you shine a light through two slits. So, if classical optics predicts that light from two pinholes shining on a lens will be focused onto two distinct spots, with no interference between the spots and with all the light from one pinhole focused on one spot, then it seems likely that quantum mechanics would predict the same thing.
Also notice that in the analysis of Afshar's experiment by W. Unruh at http://axion.physics.ubc.ca/rebel.html which scerir linked to, Unruh does not dispute Afshar's claim that all the photons from the each pinhole end up in a single detector. In fact, he offers a "simpler version of the experiment" involving a multiple pass interferometer, depicted in figure 2, and says that in this experiment you do know which path a photon took by looking at which detector it hits: "By measuring which detector they triggered, 5 or 6, one measures which of the beams, 1 or 2, the photon traveled along". Since the experiment in figure 2 is just supposed to be a "simpler version" of Afshar's experiment, it's pretty clear that Unruh would not disagree that the lens insures that knowing which detector absorbed a photon is enough to tell you which path the photon must have taken through the pinholes. Unruh is a fairly big-name physicist and his explanation of what's wrong with Afshar's conclusions about complementarity are pretty detailed, while I don't know anything about Basil Hiley and his criticisms are more vague.
Anyway, after thinking more about this experiment it's clear to me that even if the lens is enough to insure that all photons from the left pinhole end up in the right detector and vice versa, complementarity should still predict that wires placed at the interference minima will not register any hits. Consider modifying Afshar's experiment by adding extra wires at positions other than the interference minima, and sending the photons through the pinholes one-by-one. In some cases the photon will be registered at one of the wires in front of the lens, in others it will be registered at one of the detectors behind the lens. Now, if you consider *only* the subset of cases where the photon was absorbed by a wire, in these cases the photon never passed through the lens, so you have absolutely no information on which pinhole these photons went through. So if you compare the frequency that the photons hit different wires, complementarity must predict that you'll get an interference pattern--wires closer to the interference maxima will register more hits, wires closer to the interference minima will register fewer hits, and wires placed exactly at the minima will register zero. So why should an advocate of complementarity be surprised that, after removing all the wires *except* those placed exactly at the minima, these wires continue to register zero hits?
You could also turn this into a "proof-by-contradiction" that complementarity actually demands that wires exactly at the minima will not register any photons. Suppose in Afshar's experiment you sent photons through one-by-one, and found that there was some nonzero number of cases where the photons hit one of the wires at the minima. Since these photons did not make it to the lens, you have no information about which slit they went through, and so complemantarity says that the probability of finding these photons in any given location is determined by an interference pattern. But the interference pattern predicts *zero* probability of finding a photon whose path you don't know at an interference minima, in contradiction with the initial assumption that you saw a nonzero number of cases where the photon was detected at one of the wires at these minima. Thus, the only outcome consistent with complementarity is to have zero cases where the photons hit one of these wires, just as Afshar found.