DIY Quantum Eraser Experiment by the Scientific American: Is this really quantum?
This experiment can be completely explained within classical physics. It must, because laser pointers produce coherent states which exactly match the predictions of classical electrodynamics. However, it is a very good analogy for the paradoxes you would face in a quantum eraser experiment with an electron beam.
The reason the analogy is good is because the light in the classical treatment is described by a wave equation that is very similar to the Schrödinger equation for a single massive particle. Thus, wavefunctions will diffract to create single blobs if given a single slit, and interfere to make fringes if given two slits. You can further encode two different waves in a single particle using a spin-½ degree of freedom, in a manner exactly analogous to the polarization degree of freedom of an EM wave.
We don't find this situation paradoxical in classical mechanics because the light shining on the screen can't be seen as a number of discrete 'packets', and its intensity comes in a continuum. It does not make sense to ask "where did the light that makes this bright fringe come from?" because it comes from both slits. If you place a detector on each of the slits, you do observe half the power going through each slit. Within classical physics, this occurs no matter how low the laser power is.
Suppose now, though, that you replace your laser for an electron gun. Since the wave mechanics remains (much) the same, the interference fringes - or lack thereof - in the wavefunction and therefore in the detection probability will not be altered. However, electrons do behave as particles fairly often. At low enough electron fluxes, you only ever measure single-electron hits on your detector, and you can ensure only a single electron is ever present in the apparatus. If you put detectors right after the slits, you don't observe half-electrons. It is here that it starts getting paradoxical: if when I observe the slits the electron is only ever in one of the two, how come the interference pattern changes if I have access to the 'which way' information? Note, though, that it's this extra layer of particleness that makes the quantum eraser weird.
Finally, what about light? Can one do a 'quantum' version of this experiment using light? After all, light also comes in photons, and you can power down your laser low enough that only single flashes will show in the screen, right? Well, for one you need to iron out a few wrinkles. For example, you need to make sure that those single flashes are indeed a property of the light and not of the detector; there exist fairly reasonable models which explain the photoelectric effect by quantizing only the atoms and not the field. This means, in particular, that you need to change your laser for a single photon source, which is a different beast altogether.
Even then, though, the experiment is not quite enough to be a paradox. The reason for this is that photons don't really have positions or trajectories or even, really, wavefunctions. They're single excitations of the corresponding classical modes, and the modes themselves exhibit interference and wave behaviour. (Indeed, the experiments where you get photons to behave like particle waves are quite different.) Thus, while you can put together a quantum eraser measurement with single photons, the situation is more complicated and calls for a more delicate analysis.