In recent years there have been a few cases in which concerns about lack of replicability led to accusations of fraud. Some of these are Baggerly and others (2005) and Coombes and others (2007). See also the post by Uri Simonsohn: ‘Just Post It: The Lesson from Two Cases of Fabricated Data Detected by Statistics Alone‘ (2012).
The errors discovered in these examples were not necessarily simple or obvious, and the examination of the problem itself required a sophisticated analysis. Interestingly, all of these were identified by noticing the lack of reproducibility rather than by replicating the experiment.
Laine and others, 2007 discuss the role of the editorial boards of scientific publications in assuring honesty by requiring reproducibility.