  Pulsar timing array experiments search for phenomena that produce angular
correlations in the arrival times of signals from millisecond pulsars. The
primary goal is to detect an isotropic and stochastic gravitational wave
background. We use simulated data to show that this search can be affected by
the presence of other spatially correlated noise, such as errors in the
reference time standard, errors in the planetary ephemeris, the solar wind and
instrumentation issues. All these effects can induce significant false
detections of gravitational waves. We test mitigation routines to account for
clock errors, ephemeris errors and the solar wind. We demonstrate that it is
non-trivial to find an effective mitigation routine for the planetary ephemeris
and emphasise that other spatially correlated signals may be present in the
data.
