> quantum theory does not make the same predictions as classical theory when it comes to classical experiments (mechanics, basic EM phenomena)Yes, it does. Do you know how the classical limit of quantum theory works? That limit is what allows us to use classical physics in the domain where it works. If that limit didn't work, we would have a serious problem with consistency.
> It only gives probabilities of results of specified experiments of certain kinds; it does not reproduce the old predictions (like definite trajectories, Moon phases or solar eclipses)
Are you aware that all of those "old predictions" can indeed be derived from quantum theory, using the classical limit I described above? The reason that works is that, in the classical limit, quantum theory predicts a probability of 1 for one result--the classical result.
> It is natural to expect of any new theory to bring new results, but demanding that it reproduces all the old ones along is too much.
You appear to have a mistaken understanding of how new theories get accepted. New theories that don't reproduce all of the predictions of the theory they replace, in the domains where the old theory is verified by experiment, are not accepted. If general relativity had not reproduced all of the predictions of Newtonian gravity in the weak field, slow motion limit, it would not have been accepted. And if quantum theory had not reproduced all of the predictions of classical physics in the classical limit, it would not have been accepted.
