Here is an excellent rundown of some soul searching in the neuroscience community regarding statistical significance. The standard method of analyzing brain scan data apparently involves something akin to data mining but the significance tests use standard single-hypothesis p-values.
One historical fudge was to keep to uncorrected thresholds, but instead of a threshold of p=0.05 (or 1 in 20) for each voxel, you use p=0.001 (or 1 in a 1000). This is still in relatively common use today, but it has been shown, many times, to be an invalid attempt at solving the problem of just how many tests are run on each brain-scan. Poldrack himself recently highlighted this issue by showing a beautiful relationship between a brain region and some variable using this threshold, even though the variable was entirely made up. In a hilarious earlier version of the same point, Craig Bennett and colleagues fMRI scanned a dead salmon, with a task involving the detection of the emotional state of a series of photos of people. Using the same standard uncorrected threshold, they found two clusters of activation in the deceased fish’s nervous system, though, like the Poldrack simulation, proper corrected thresholds showed no such activations.