The biggest potential danger is potentially a massive breakdown in relations between Copts and Muslims in Egypt.
The person who comes out of all this looking smartest is Samuel Huntington. His book on the “clash of civilizations” was widely and unfairly trashed as predicting an inevitable conflict between Islam and the west, and he was also accused of ‘demonizing’ Islam. That’s not what I get from his book. As I understand it, Huntington’s core thesis was that while good relations between countries and people with roots in different civilizations are possible and ought to be promoted, civilizational fault lines often lead to misunderstandings and tensions that can (not must, but can) lead to violence and when conflicts do occur, civilizational differences can make those conflicts worse.
Unfortunately, Islamic radicals are deliberately hoping to promote a clash of civilizations in the belief that a climate of polarization will strengthen their political power in the world of Islam. Attacking the embassy in Cairo is an effort to push Egyptian opinion in a more radical direction, but the radicals hope that this is part of a larger push that will bring them to power across the Islamic world. Like Boko Haram in Nigeria, which hopes to provoke a religious war with the Christians partly in order to achieve power in the Muslim North, radicals use the prospect of a clash of civilizations to further their own cause throughout the troubled Islamic world.