We analyze the uncertainties and possible systematics associated with the "Dark Flow" measurements using the cumulative Sunyaev-Zeldovich (SZ) effect combined with all-sky catalogs of clusters of galaxies. Filtering of all-sky cosmic microwave background maps is required to remove the intrinsic cosmological signal down to the limit imposed by cosmic variance. Contributions to the errors come from the remaining cosmological signal, which integrates down with the number of clusters, and the instrumental noise, which scales with the number of pixels; the latter decreases with integration time and is subdominant for the Wilkinson Microwave Anisotropy Probe (WMAP) 5 year data. It is proven both analytically and numerically that the errors for the 5 year WMAP data are μK per dipole component. The relevant components of the bulk flow velocity are measured with a high statistical significance of up to 3-3.5σ for the brighter cluster samples. We discuss different methods to compute error bars and demonstrate that they have biases that would overpredict the errors, as is the case in a recent reanalysis of our earlier results. If the signal is caused by systematic effects present in the data, such systematics must have a dipole pattern, correlate with cluster X-ray luminosity, and be present only at cluster positions. Only contributions from the SZ effect could provide such contaminants via several potential effects. We discuss such candidates apart from the bulk motion of the cluster samples and demonstrate that their contributions to our measurements are negligible. Application of our methods and database to the upcoming PLANCK maps, with their large frequency coverage, and, in particular, the 217 GHz channel will eliminate any such contributions and determine better the amplitude, coherence, and scale of the flow.
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