I dunno, the Asch conformity experiment seems to suggest that people will doubt the evidence of their senses if enough peer pressure is applied. Combine that with general unreliability of memory formation and maybe you could explain away tens of thousands of people all claiming to have experienced the same weird phenomenon.
I posited the mass hysteria explanation before I read up on Fatima, but I think on balance I still believe more in mass failures of human senses and cognition (which I already know is pretty buggy) than in weird supernatural phenomena.
The asch conformity experiment, it should be noted, makes people say they see a line as slightly longer than it actually is.
One of the explanations in the irrationality game thread for UFOs and other paranormal events seen by multiple people at once, like the was mass hysteria. This is also a common explanation given for any seemingly paranormal event that multiple people have independently witnessed.
But mass hysteria is mostly known from incidents where people hysterically believe they have some disease, or have some hysterical delusion (false belief). In cases where people report seeing something or having a hallucination, it tends to be a few people across a large society. For example, when reports of Spring-Heeled Jack were going around England, multiple people claimed to have seen Spring-Heeled Jack, but there were no cases of hundreds of people seeing him simultaneously; therefore, the hysteria could have selected for people who were already a little bit crazy, or it could just have been that out of millions of English people a few of them were willing to say anything to get attention.
Conformity pressures can cause people to misinterpret borderline perceptions - for example, if someone says a random pattern of dots form Jesus' face, I have no trouble believing that, thus primed, people will be able to find Jesus' face in the dots. But it's a much bigger leap to assert that if I say "Jesus is standing right there in front of you" with enough conviction, you'll suddenly see him too.
Does anyone have any evidence that mass hysteria can produce a vivid hallucination shared among multiple otherwise-sane people?