Error correlations in current GRACE monthly gravity field models strongly affect the errors of inferred regionally averaged mass variations (RMV). To demonstrate this, we develop an empirical method which roughly estimates scaling factors to convert error bars computed by ignoring error correlations into more realistic error bars for RMV. For current solutions by CSR and GFZ, we find factors in the order of 2 or more for near-polar regions and below one for near-equatorial regions. A comparison of RMV computed from the CSR and the GFZ models for Greenland, Antarctica and the Amazon basin supports our findings. We discuss consequences on error assessment and error separation. For example, previously published GRACE-derived RMV of Greenland may be still strongly affected by errors in the GRACE products.