  We use stellar proper motions (PM) from Gaia Data Release 2 for studying the
internal kinematics of Milky Way globular clusters. In addition to statistical
measurement errors, there are significant spatially correlated systematic
errors, which cannot be ignored when studying the internal kinematics. We
develop a mathematically consistent procedure for incorporating the spatial
correlations in any model-fitting approach, and use it to determine rotation
and velocity dispersion profiles of a few dozen clusters. We confirm detection
of rotation in the sky plane for ~10 clusters reported in previous studies, and
discover a few more clusters with rotation amplitudes exceeding ~0.05 mas/yr.
However, in more than half of these cases the significance of this rotation
signature is rather low when taking into account the systematic errors. We find
that the PM dispersion is not sensitive to systematic errors in PM, however, it
is quite sensitive to the selection criteria on the input sample, most
importantly, in crowded central regions. When using the cleanest possible
samples, PM dispersion can be reliably measured down to 0.1 mas/yr for ~60
clusters.
