Well, I'm a foreign policy guy, so I'll offer a concern or two based upon what I know of his worldview.....
He seems like the type who may find friends within the neoconservative movement. I think his views of the Middle East are obviously a product of his experiences on 9/11, as he sees democratization as the ultimate answer to the problems of terrorism. Any kind of regional view such as this really worries me -- it has gotten us into Iraq, no? -- and he seems vulnerable to the grandeoise ideas of overthrowing the current order, by force if necessary. A fiercely pro-Israel partisan, I'm not sure if he would represent an ideological departure from what we have in the White House, DoD, and VP's office now.
His downside? I'll let somebody who's more in tune with domestic affairs answer this, but there are concerns about his past personal life.
And more than anything, I've heard from many sources that he surrounds himself with "yes" men and does not tolerate dissent. Whether that's foreign policy or domestic, that kind of attitude is very troubling to me.
If he can navigate the GOP obstacle course and emerge victorious from the first few southern primaries, he's got a shot.
IMO, Rudy's greatest strength is his skill as a manager. He is incredibly organized and focused and has a knack for getting his staff to ahere to his governing philosophy and implement his policies. While the NYC government is not on the same scale as the executive branch of the federal government, those organizational and managerial skills that he showed as mayor will also benefit him greatly as President. I guaranteee his message will be coherent and consistent, and his cabinet will speak with one voice.
Obviously Rudy's political weakness is his past personal behavior. However, he built up a lot of political capital in the days and months following 9/11, so most people will probably be willing to look past his indescressions. If he is head-to-head against Clinton, Hillary will not be able to effectively use Rudy's personal conduct against him; voters will see it as hypocritical because of her husband's behavior. That may not be fair to Hillary, but its political reality.
Another challenge Guiliani will have to overcome is his ties to the big-business/ Wall Street wing of the GOP. He has to show that he can relate to middle class and blue collar voters. Again, his leadership following 9/11 and his support of firefighters, police, etc went a long way in building trust with middle income voters.
Guiliani is the embodiment of tough-love conservatism; some would say he's liberal on a few issues. He has broad appeal and likeability and is acceptable to many Democrats. I think its highly likely he will be President.
It's going to be quite the race. He has some pretty tough competition. I don't know.
I think when anyone in government thinks they know best about the war they should be out taking polls of what the people think. I don't think there is one solution to that problem. I haven't done much reading into the next president yet but this is a good blog :O)