My working hypothesis for the moment is that a group of terrorists (Al Qeida or other) managed to get hold of a very small quantity of Anthrax spores, and to smuggle this in to the USA. The tabloid offices targeted because they were certain that would be a high profile target that would be hyped in the weeks following.
In order to achieve maximum panic and terror effect, this action was accompanied by mailing a large number of packages containing one or more types of white powder (instant milk? flour? lime?) to a widely dispersed set of targets. These were probably mailed over several days to assure that there would be a continuous flow of news stories to keep the panic impact at a maximum.
Assuming that the terrorists did not have the ability to make the Anthrax spores themselves, this becomes an extremely low-tech, low-cost terrorist attack. True, not many people are killed. But it is a mistake to assume that mass murder is the sole objective of terrorists. Fomenting mass panic works for them as well.
The proper response should be neither panic nor glib denial. Anyone receiving a suspicious package should contact the authorities, and they will be handling it just as they have in this and the other stories that have been posted.