I think the publish or perish academic culture makes it extremely susceptible to glossing over things like this - especially for statistical analysis. Sharing data, algorithms, code and methods for scientific publications will help. For papers above a certain citation count, which makes them seem "significant", I'm hoping google scholar can provide an annotation of whether the paper is reproducible and to what degree. While it won't avoid situations like what the author is talking about, it may force journal editors to take rebuttals and revisions more seriously.

From the perspective of the academic community, there will be lower incentive to publish incorrect results if data and code is shared.