The "Ozma problem" was coined by Martin Gardner in his book "The Ambidextrous Universe", based on Project Ozma. Gardner claims that the problem of explaining the humans left-right convention would arise if we enter into communication (by radio waves, no images allowed) with life on another planet. We can ask the aliens to perform any experiment they want. It is claimed that the classical experiments with magnets, electrical currents, light polarization, gyroscopes etc. can't solve the problem. The only simple experiment that solves the problem is the beta decay in which the parity is not conserved and this can be used to distinguish humans left-right spatial relations. But all this are quite old, the parity violation in weak interactions was experimentally proved in 50s by Chien-Shiung Wu. I was wondering if something has changed since then and if there are some other experiments (maybe some thought experiments) and theories that can solve the Ozma Problem.
I haven't read that book, but I did read Feynman's discussion of (sounds like) exactly the same thing. Easy: Tell the aliens how to build a telescope, then describe the configuration of some galaxies near them. OK OK, but suppose we rule that out: We can't see any objects in common. Easy: Send them circularly-polarized radio waves (thanks @Anonymous Coward). OK OK, let's say our radio waves must be linearly polarized. Easy: Tell them to look at almost any phenomenon related to the weak force, for example the beta-decay of cobalt-60 in a magnetic field. But then there's one more catch--what if the aliens are made of antimatter and they actually were watching the beta-decay of antimatter-cobalt-60? In Feynman's discussion (if I recall correctly), that's where it ends: There's no way to be really sure that the aliens understand right and left correctly, because they may be made of antimatter.
But since 1964, when CP-violation was observed, we can even eliminate that possibility: We tell the aliens how to watch kaons decay (for example) and then the aliens can figure out whether they're made of (what we call) matter or antimatter, and therefore they can figure out which way is left and right without any more ambiguity. So I guess that aspect is a slight update from pre-1964 descriptions.
Watching atoms decay in a magnetic field is a pretty simple thing to do by the standards of particle-physics experiments. I don't know of any parity-violating experiments that are much simpler than that. It just has to involve the weak force.