Thanks to ZapperZ for bringing this to my attention. This paper is about to appear in Phys Rev Letters, and argues that the Lorentz force law (as written to apply to magnetic materials, not isolated point charges) is incompatible with Special Relativity. The argument includes a simple thought experiment. In one reference frame, you have a point charge and a little piece of magnetic material. Because the magnet is neutral (and for now we ignore any dielectric polarization of the magnet), there is no net force on the charge or the magnet, and no net torque on the magnet either. Now consider the situation when viewed from a frame moving along a line perpendicular to the line between the magnet and the charge. In the moving frame, the charge seems to be moving, so that produces a current. However (and this is the essential bit!), in first year physics, we model permanent magnetization as a collection of current loops. If we then consider what those current loops look like in the moving frame, the result involves an electric dipole moment, meaning that the charge should now exert a net torque on the magnet when all is said and done. Since observers in the two frames of reference disagree on whether a torque exists, there is a problem! Now, the author points out that there is a way to fix this, and it involves modifying the Lorentz force law in terms of how it treats magnetization, M (and electric polarization, P). This modification was already suggested by Einstein and a coauthor back in 1908.
I think (and invite comments one way or the other) that the real issue here is that our traditional way to model magnetization is unphysical at the semiclassical level. You really shouldn't be able to have a current loop that persists, classically. A charge moving in a loop is accelerating all the time, and should therefore radiate. By postulating no radiation and permanent current loops, we are already inserting something fishy in terms of our treatment of energy and momentum in electrodynamics right at the beginning. The argument by the author of the paper seems right to me, though I do wonder (as did a commenter in ZZ's post) whether this all would have been much more clear if it had been written out in four-vector/covariant notation rather that conventional 3-vectors.
This raises a valuable point about models in physics, though. Our model of M as resulting from current loops is extremely useful for many situations, even though it is a wee bit unphysical. We only run into trouble when we push the model beyond where it should ever have been expected to be valid. The general public doesn't always understand this distinction - that something can be a little wrong in some sense yet still be useful. Science journalists and scientists trying to reach the public need to keep this in mind. Simplistically declaring something to be wrong, period, is often neither accurate nor helpful.