Well, aside from the problem that information can't be created from thin air. You can fix certain lens errors, but you cannot extract details that aren't there on the original.
The most obvious consequence is that you can't use this technique to extract more megapixels than the sensor has.
Less obvious limitations might be the sensibility to noise; all these samples have been taken in bright light, but if your crappy lens produces a very noisy image in low light, this method won't fix it.
Furthermore, the numerical aperture (NA) of the lens defines the highest possible resolution. Even with this method you can't get a higher resolution than wavelength/NA.
Unfortunately, there's no way around the principle "Garbage in, garbage out." Lensmakers rejoice, your business wasn't made obsolete after all!
Nevertheless, I can see exciting applications for this method; one thing that comes to mind are improving the pictures taken by photographic scanners used for digitizing old books.