Apparently particles can be anywhere when not observed. How strong is this theory really? Okay the wave-function can be collapsed through observation but how are we so sure that when an object is not being observed that it is in potential states? How are we so sure whether or not the wave function is collapsed by a conscious observing force other than us? And is superposition an assumption due to the fact that when we observe waves they act as particles, so we assume that everything has different potential until measurement; when really we don't know for sure whether it is that an object is in potential states or a conscious observance by a higher power already puts things in order already eliminating this potentiality?
As Hunter already remarked we can't say by no means that Quantum Mechanics is a complete theory, nevertheless a lot of experimental observations agree with QM predictions and on the other hand I don't think that there exists another theory which predicts so many phenomena in agreement with the experiments. (So that you may explain some "quantum" effects with a classical ad hoc theory, but you won't explain a lot of other "quantum" effects with it.)
Having said this, a strong experimental evidence of the existence of superposition is given by subsequential Stern-Gerlach filters. In short you filter a stream of spin 1/2 particles by measuring their spin along the z-axis and taking only the ones with positive component, then you do the same for the x-axis and you measure the z-axis spin again, you see that particles with negative component of z-axis spin reappears. If you look for a classical explanation of the measurement process (such as the measurement outcome is undeterminate because we don't know the pre-measurement state) you will have some problems in interpretating this regeneration. On the other hand the superposition explains this phenomena in a neat way: the superposition of states is a distinct state on its own, and not just an "unknown but determinate" state of the superposition.