The theoretical upper limit of the resolving power of the human eye will be given by the Rayleigh criterion. For a pupil diameter of 5mm and a wavelength of 500nm (green light) we can theoretically resolve about 1.22e-4 radians. 1 arcsecond is about 5e-6 radians, i.e. 25 times smaller than we could theoretically resolve without a magic retina.

1 arcminute is a more realistic size for what people can reliably resolve I think. I guess we need significantly better than that to avoid a subjective feeling it is blurry but, that is about what we can actually reliably tell the difference between I think. We cannot tell the difference below 25 arcseconds or so though, it is not possible without larger pupils.