The chief problem with the 'explosions all over the world' change is that there would be that in the book, when it was just New York getting cut in half, the sympathy was the catalyst driving the unity of the world. With everybody dying the movie will have to work very very hard to make us believe that the world's leaders will just say 'whoops, all our people are dead, WORLD PEACE NOW.'
Again though, if the threat is painted as a sufficiently alien attack, and not as just a bunch of bombs going off, it might not be that hard to change the catalyst from sympathy to pure fear.