  The NRAO VLA Sky Survey (NVSS) Rotation Measure (RM) catalogue is invaluable
for the study of cosmic magnetism. However, the RM values reported in it can be
affected by n$\pi$-ambiguity, resulting in deviations of the reported RM from
the true values by multiples of +-652.9 rad m-2. We therefore set off to
observationally constrain the fraction of sources in the RM catalogue affected
by this ambiguity. New broadband spectro-polarimetric observations were
performed with the Karl G. Jansky Very Large Array (VLA) at 1--2 GHz, with 23
n$\pi$-ambiguity candidates selected by their peculiarly high |RM| values. We
identified nine sources with erroneous RM values due to n$\pi$-ambiguity and 11
with reliable RM values. In addition, we found two sources to be unpolarised
and one source to be inconsistent with neither n$\pi$-ambiguity nor reliable RM
cases. By comparing the statistical distributions of the above two main
classes, we devised a measure of how much a source's RM deviates from that of
its neighbours: $\Delta/\sigma$, which we found to be a good diagnostic of
n$\pi$-ambiguity. With this, we estimate that there are at least 50 sources
affected by n$\pi$-ambiguity among the 37,543 sources in the catalogue.
Finally, we explored the Faraday complexities of our sources revealed by our
broadband observations.
