I think the most destructive effect after the ionizing radiation permeated the atmosphere would be the massive pan-geographic lightning and electrical discharges which would occur. These would neutralize the charge in the atmosphere, and probably devastate the surface of the Earth, killing everything that conducts electricity to the ground, and setting widespread fires that consume all the available oxygen. The ozone layer would be gone, so anything left would be burned in seconds by the Sun's ultraviolet rays. Telecommunications would be impossible because the ionosphere would go totally berserk.

Pretty horrifying eh?