I think it should be said that, whether or not the specific treatment regimen being contemplated here works at all reliably, we are not deep in the land of woo here. There are good theoretical, and empirically backed reasons to think that it is likely to be possible to remediate and improve visual function through some form of eye exercise. There is a shitload of evidence that skillfully, cognitively controlled eye movements play a very large role in normal vision, and that the skills and useful habits in question are, at least partially, learned rather than innate. Generally speaking, sensori-motor skills can be much improved by appropriate practice, and there seems to be no good reason why that should not apply to visual skills just as much as to, say, catching a ball.
The problem here, however, is that we do not yet know enough in detail about the issues to be able to say reliably what sort of exercise regime will actually be helpful. At present, people can do little better than guess, and use a scattershot approach of exercising as many aspects of eye movement as you can think of an exercise for. It might well be, however, that quite different exercises might be appropriate for different individuals, depending on the detailed specifics of their visual problem. What works for one patient might be useless, or even, conceivably, actively harmful, for another. (This might explain why Ceejaytee’s and ZenBeam’s sons, and others, might truly have been helped, even though large scale studies apparently show little sign, on average, of any benefit.) Another possibility is that most people reach ceiling, get as good as they are going to get or need to get with the relevant skill, at a fairly early age, after which there is little room for further improvement. A few individuals with particular problems might benefit from appropriate eye exercises, but they are going to be a complete waste of time for most. Unfortunately, we do not yet understand the role of eye movements in vision anything like well enough for us to be able to say who might benefit from eye exercises, or what those exercises might be.
I must say, that the fact that the optometrist seen by Unintentionally Blank’s son has written a book called What Your Bright Child Can’t See does not fill me with confidence. That is just the sort of title that a con man might use to hook gullible parents with the hope that their underperforming child is in fact, underneath it all, the hidden genius they always hoped for, and that the genius will start to blossom forth as soon as they cough up the hefty treatment fees. On the other hand, as Broomstick mentions, for some visual problems there is a relatively short window of time during which they can be successfully amelioated, and if things truly are fixable, and you do not get them fixed soon, your kid may be out of luck. In practical terms, I can only give the advice that several others have: get a second (and maybe even a third) opinion from a real opthalmologist, and follow their advice.
By the way, this Wiki page might be helpful: http://en.wikipedia.org/wiki/Eye_exercises