Jonah Lehrer wrote about the (surprising?) power of publication bias.
http://m.newyorker.com/reporting/2010/12/13/101213fa_fact_lehrer?currentPage=all
Cosma Shalizi (I think) said something, or pointed to something, about the null model of science - what science would look like if there were no actual effects, just statistical anomalies that look good at first. I can't find the reference, though.
To me it seems pretty obvious that we are doing that, and have been for many decades. But I suppose spelling out an argument for this conclusion suitable for a general audience would require bridging some significant inferential distances.