This paper develops concentration inequalities that can be used for finite-sample inference of moment condition models. The statistics are similar in spirit to Kolmogorov-Smirnov tests; analysing regional differences between the empirical distribution function (EDF) and the distribution function implied by the moment conditions. Implied probabilities present an information-theoretic tool to estimate such a distribution function. Model misspecification due to parameter instability yields systematic differences in the behaviour of generalised empirical Likelihood (GEL) implied probabilities relative to the EDF weights. Parameter heterogeneity may therefore be identified by the contrast of GEL implied probabilities and the EDF over regions of the sample space partitioned by characteristics suspected to be driving the heterogeneity. Data-driven methods can carefully select partitions that pick out points that are inconsistent with the moment restrictions. Using VC theory, tail bounds are provided for maximum deviations of the sum of GEL implied probabilities from their empirical average.