Was the (unintended?) duping of the American public by Welles' Halloween broadcast something that could have happened only in the 1930s? Have citizens become more sophisticated in their consumption of media?
While the era in which "The War of the Worlds" was initially broadcast that evening of October 30, 1938, undoubtedly contributed to the mass hysteria that resulted from fears of an alien invasion, it is not unreasonble to suggest that such a reaction could have occurred during any period since then, right up to the present.
A similar broadcast during the early 1940s would likely have tapped into the public's paranoia about foreign invasion stemming from the actual activities of German espionage agents on U.S. soil and the presence of Japanese submarines off the U.S. Pacific coast. Especially in the days following the attack at Pearl Harbor, Hawaii, paranoia regarding a Japanese invasion was great, and "ghost" sightings of enemy submarines and paratroopers were not uncommon. Had "The War of the Worlds" been broadcast during that period of time, it most definitely could have had a similar impact on the public.
The post-World War II era was characterized by wide-spread fear of communism, a more subtle and pervasive threat that allowed for greater psychological reactions that would have resulted in mass hysteria following a misunderstood radio broadcast. Fear of communism and of the Soviet Union, reached a peak with that country's detonation of its first atomic bomb in 1949, the same year the Communists took power in China. In fact, the 1956 science fiction horror movie "Invasion of the Body Snatchers" was an allegory of the paranoia surrounding the fear of communist infiltration into American society. The so-called "Red Scare" as personified by Senator Joseph McCarthy provided a perfect environment in which a broadcast like "The War of the Worlds" would have been misinterpreted as an actual event.
Whether something similar could happen today is debatable, but it probably could, especially in the wake of the terrorist attacks of September 11, 2001, when fear of terrorists on U.S. soil ran wide and deep. Few Americans would likely believe in an invasion from outer space, but a little tweaking of the text, with "Martians" replaced by "Muslims" could have a similar effect, unfortunately.