Methods to detect published mistakes without raw data? I'm interested in ways to detect mistakes in published papers without analyzing the raw data. For example the GRIM test [1]. Here's another similarish one from one of the GRIM authors' blog. I don't know of any others. 
Looking for inconsistencies in reported stats seems attractive, because digging through raw data is difficult and sometimes the data isn't available. It's probably also easier to automate.
Edit: Benford's law, credit to DJohnson. Any others?

[1] Brown et al., A Simple Technique Detects Numerous Anomalies in the Reporting of Results in Psychology, Social Psychological and Personality Science (2016)
 A: You could simply ask for the data if you think there is an error. If they say no that would be a concern to me, although I find it hard to believe people would falsify results deliberately (well some will, but that will be rare I think).
A: Below are heuristics that are not necessarily direct mistakes, but are frequent ways of using statistics sub-optimally.
Use of underpowered statistical tests, do they mention sample size calculations for example?
Data dredging especially on “big data”. If all variables are highly significant this could be a sign of stepwise regression or similar being used, rather than more logical reasoning having been used.
Over reliance on hypothesis tests, as we as consumers of the paper do not know how many other tests were tried, and compensation schemes for multiple comparisons have side effects such as depending on how many (acknowledged) tests were performed. Further, some fields have much prior knowledge which if not encoded into a test through say a Bayesian approach, are too prone to randomness of “significant” results of hypothesis tests.
Not using multiple imputation or similar but instead dropping observations with missing values from the analysis may bias the remaining data, and also reduces the power of subsequent tests.
Something that is more difficult to discern is if the techniques used are not well understood by the authors. This can be more apparent if they give a presentation of the paper. If the technique is not understood sufficiently, it may have been misused.
