Does QM mean that NM is wrong? That's what one might at first think, and that's the sort of thing that a lot of simplistic science journalism would make one think ("New results overthrow longheld theory!!!"). But NM had been extensively tested over the previous centuries, and for the most part, it had been a great success. So it must not be completely wrong.
Asimov  The Relativity of Wrong has a good discussion of this issue.
So let us look more closely at the relationship between QM and NM. In the limit of actionlike quantities much greater than Planck's constant h, QM becomes NM. That is evident from these three formulations:
 Schroedinger > HamiltonJacobi
 Heisenberg > Hamilton
 Feynman pathintegral > EulerLagrange
So NM is an approximation that is only good for (actionlike) >> h, what's often called the classical limit.
This explains why NM had been so successful before the development of QM. It had been successful because it was applied to systems where actionlike quantities are much greater than h, and those systems are just about everything much larger than an atom.
The same is also true of relativity. NM is also a limiting case of it, and one can quantify how far off it is rather easily. Approximately (1/2)*(v/c)^{2}, where v is typical speeds, and c is the speed of light in a vacuum, a speed related to the geometry of spacetime. Special relativity and quantum mechanics make relativistic quantum field theory, and that reduces to NM in two ways, through nonrelativistic QM and through classicallimit special relativity:
RQFT > NRQM > NM
RQFT > SR > NM
So if some theory is going to succeed in superseding QM, or more precisely, RQFT, it must have the same relationship to QM that QM has to NM. It must be a superset theory that reduces to QM in some appropriate limit, a limit where QM has been successfully tested.
Pseudoscientists and crackpots often get into trouble over this. They often make little effort to show that their theories account for what existing theories successfully account for.

One last thing. The classical limit of QM is a bit more complicated than what my discussion of it here may suggest. In a way, it has not one but two classical limits: the particle limit and the wave limit. Here is how they related to QM:
Particle limit. The familiar sort of physical objects are all in this limit. Their wavefunctions' extents are much, much, much smaller than their sizes.
QM statistics: Nonissue. The wavefunctions are too small to overlap, and macroscopic objects are almost always nonidentical at the elementaryparticle level.
Wave limit. Or more generally, the field limit. Electromagnetism and gravity are wellknown fields in this limit, and this limit also includes collective effects like sound waves and BoseEinstein condensates.
QM statistics: always BoseEinstein.