Binary response index models may be affected by several forms of misspecification, which range from pure functional form problems (e.g. incorrect specification of the link function, neglected heterogeneity, heteroskedasticity) to various types of sampling issues (e.g. covariate measurement error, response misclassification, endogenous stratification, missing data). In this article we examine the ability of several versions of the RESET test to detect such misspecifications in an extensive Monte Carlo simulation study. We find that: (i) the best variants of the RESET test are clearly those based on one or two fitted powers of the response index; and (ii) the loss of power resulting from using the RESET instead of a test directed against a specific type of misspecification is very small in many cases.