A buddy of mine ripped out his toe piece and I think the cause was the same issue you have. I looked at that ski and his other ski and the heel piece on his pulled-out ski as well as the nose and heel piece on his ok all seemed to have a bit of space/play between the binding and ski under the screws. Although he is a very big guy he's not a particularly good skier and I saw the crash where he pulled out the toe piece and there is no way the binding should have come out. Basically the shop tech who mounted them must have been drunk, stoned and/or an idiot. Took the skis back to the store and they immediately remounted all his binding pieces. You should do the same.
If the binding screws haven't gone deep enough then they won't have as much area to distribute the load across the screw/ski interface, which will make the bond weaker straight off. Also, if there is a bit of play then this can lead to uneven load distribution and bigger stress concentrations which can result in failure at much lower forces. Also the binding/ski interface will be at lot less stiff, about 1/4 to 1/5 of the stiffness depending on the way the load is transferred from the binding to the ski. The factor of 1/4 or 1/5 is due to what Engineers would call a change in effective boundary conditions from a clamped plate/beam to a hinged plate/ beam. Yes... I'm a geek (doing a PhD in Mechanical Engineering).