I saw "The Day After Tomorrow" too and was... underwhelmed by the sheer amount of bad/hollywood science in it. My feelings about the film were reinforced when I came across
this site and the comments therein. My goodness, this film seems to be second only to "The Core" in sheer scientific impossibilities.
Okay. Yellowstone.
Should it erupt, things will become... difficult. America will become a borderline nation due to the sheer devastation that such an eruption (with associated flying molten rock, rivers of lava, destructive ground tremors etc) would cause. Air travel would be impossible (except
maybe for zeppelins and other lighter-than-air craft) while long-distance ground travel would become very hard due to the choking effect of ash. Effectively, America would cease to be a superpower and would, at best, become a barely-better-than-subsistance area. At least until the ash settles, whereupon the ground will become extremely fertile. May take a while, though.
The rest of the world would also suffer. The amount of sunlight reaching the ground would be reduced due to the ash cloud, leading to a rapid amount of global cooling and possibly inducing another ice age. The ash cloud would also affect air travel across most of the northern hemisphere (and across South America), reducing trade, travel etc. The resulting population drop would not be as extreme as in America, but it would be severe.
China would most likely be the least affected and may choose to use the crisis as an opportunity for expansion. A similar rationale may be seized upon by the Islamic countries, so open warfare would be a highly likely result. Should it go nuclear, extinction becomes a distinct possibilty for much of life on earth, including humanity.
Let's hope that the scientists gfind some way to lower the pressure under Yellowstone. Perhaps by drilling down and starting to pipe out some of the accumulating magma?
Well, whatever happens, happens, and we'll just have to cope.
Hope I haven't depressed you all too much.