Emergency preparedness, yes. Terrorism, no.
My opinion on his understanding of terrorism is based on a Time magazine article linked to the title of this post. He mocks the threat of North Korea because they never directly orchestrated an attack on U.S. soil. He apparently doesn't know that they sell weapons to people who do.
Guiliani thinks that the Iraq war reduces the terror threat in the U.S. What? The increased resentment towards the U.S. brought on by that war is bringing more recruits. Guiliani complains about the Clinton Administration track record on terror. At least Bill Clinton tried to bomb Osama bin Laden, and at a time when he was under severe personal attack.
Besides, I have some serious doubts about the quality of his character. Imagine running a campaign on "commitments" to the American public when your marriage failed in part because of your infidelity. The man is blind to himself. And of course there is the appointment of Bernard Kerik, a man who used the deaths of brave men and women to get a cool love nest for his mistress.