I don't see why we should ascribe any particular significance to the name "virtual" ... that name was assigned by a human (or humans) after all, and we hardly have a stellar record with naming conventions. I have seen several posters on here go on multi-post rants about the stupid and confusing names and conventions that are accepted in physics. I am not nearly so passionate about it, but I do think that just because a particle is called "virtual" does not inherently prevent it from being a detectable physical object.
"Virtual particles" is the catch-all name we give to the entities that bind quarks together inside nucleons, and those that bind electrons in atoms, so I personally think they are very real. If the standard model is correct, and gravitons exist, then I think that would also likely mean that the planets are held in their orbits by "virtual particles".
As I said before, it is not clear to me why virtual particles would be characterized as a "mathematical approximation" ... approximation to what? (You didn't really answer this the last time I posted it

). I thought they were a consequence of the necessary symmetry of the relativistically correct expression for energy: E
2=(pc)
2 + (mc
2)[SUP2[/SUP], which led Dirac to postulate the "Dirac sea" of "vacuum fluctuations". Anyway, I don't think that QED could explain much without virtual photons to carry the electromagnetic force, so they seem pretty physical to me ... perhaps they are just poorly named?
Regarding the Casimir effect, it seems to me that the jury is still out on that one. It is a beautiful idea, but as far as I know, there is no definitive proof that can distinguish the Casimir effect from van der Waals forces.