In The New Cosmic Onion, I read the following:
If mirror symmetry were an exact property of Nature, it would be impossible to tell whether a film of an experiment has been made directly or by filming the view in a mirror in which the experiment has been reflected. This is equivalent to saying that Nature does not distinguish between left and right in an absolute way. This is the case for phenomena controlled by gravity, the electromagnetic, or strong forces. As these control most observed phenomena, it had been assumed that left-right symmetry is an inherent property of all subatomic processes. But in 1956 mirror symmetry was discovered to be broken in weak interactions.
How does the following situation with electromagnetism follow mirror symmetry? A positively charged particle travels upwards in the plane of the screen, and a magnetic field points to the right in the plane of the screen. By the right-hand rule, we see that the particle experiences a force into the screen. However, when we reflect this situation left-to-right across a plane perpendicular to the screen, the right-hand rule then tells us that the particle experiences a force out of the plane of the screen.
So what gives?