Another problem as I see it is the law of supply and demand. Assuming that quality schools are a scarce resource, it's clear that the government can't simply distribute this resource to more people simply by legislative fiat. In the Cleveland case, the voucher law allowed students to attend suburban public schools, but not one agreed to participate in the program, thus making the pool of "quality" schools even smaller (in fact, most of the participating schools in Cleveland are religious, a question I don't think the justices addressed adequately). The mere fact that more people can afford an alternative school doesn't increase the capacity of those schools; there may not to be room for everyone who wants to attend a better school, so they might be stuck in a lousy school irrespective of economic status. And jamming more and more kids into the "good" schools may well disrupt the very factors that make them good--low class size, for example. Finally, if more and more students are competing for this scarce resource, the price is likely to go up, an event that might not be covered by a voucher program.
Dodd at Ipse Dixit points out another potential flaw with the voucher concept:
There are other potential problems, of course, not least of which is that with government aid inevitably comes government control. Avoiding such pitfalls is essential for vouchers to work.
Exactly; and a desire to avoid such control could lead schools not to participate in the program, so there you have supply problems again.