Well, that's not actually "diffraction".
The fuzzy edge of the moon, and the added glow that's sometimes seen
around it, are all effects caused by the light passing through air before it
reaches you.
This gives you some idea of why astronomers go to such effort and
expense to get their telescopes above as much of the atmosphere as
possible ... placing all serious observatories on mountaintops, and even
putting telescopes in orbit. It's all because the air does such a job on the
light that's trying to shine through it. We have to make do with whatever's
left over after that.
