Gross flows represent transition counts between a finite number of states for individuals in a population from one point in time to the next. Such flows are important for researchers and policy analysts; for example, gross labour flows for understanding labour market dynamics. Unfortunately, the observed flows are typically subject to classification error. As a result, the problem of adjusting observed flows for classification error has received considerable attention. Currently, three methods for adjustment of classification error are available. All these methods use the key assumption of independent classification errors (ICE) in conjunction with interview-reinterview data. We first give modifications to two of the methods that ensure that margins of the adjusted flow table agree with the published “stocks” without requiring a final margin adjustment. We then propose e-response contamination models and procedures for studying the robustness of ICE under different scenarios of departures from ICE applicable for all the methods. Our empirical results, based on data from the Canadian Labour Force Survey, show that for many scenarios the ICE assumption is fairly robust. There are, however, situations where this is not the case. We thus suggest that users apply the proposed procedures to check the robustness of ICE under scenarios relevant for their own applications. Finally, we provide valid chi-squared tests for modeling flow tables adjusted for classification error under ICE so that the adjusted flows could be further smoothed under the model. These tests are also illustrated using data from the Canadian Labour Force Survey.