My impression is that most scientists feel that they don't make very many errors in reporting their results. My own experience from coding tells me that I make many simple mistakes.
One very simple check for mistakes in a published paper is to see if the reported statistic value matches the reported p value. For example, if we see "t(15) = 2.3; p = 0.034” we can check if the p value for t=2.3, with 15 degrees of freedom, really is 0.034. Obviously, this check cannot tell us about other problems that might have lead to an inflated t (etc) value. Nevertheless, nearly 20% of reported statistics failed this test in a sample from the psychology literature:
http://dx.doi.org/10.3758/s13428-011-0089-5
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