  Signals from radio pulsars show a wavelength-dependent delay due to
dispersion in the interstellar plasma. At a typical observing wavelength, this
delay can vary by tens of microseconds on five-year time scales, far in excess
of signals of interest to pulsar timing arrays, such as that induced by a
gravitational-wave background. Measurement of these delay variations is not
only crucial for the detection of such signals, but also provides an
unparallelled measurement of the turbulent interstellar plasma at au scales. In
this paper we demonstrate that without consideration of wavelength- independent
red-noise, 'simple' algorithms to correct for interstellar dispersion can
attenuate signals of interest to pulsar timing arrays. We present a robust
method for this correction, which we validate through simulations, and apply it
to observations from the Parkes Pulsar Timing Array. Correction for dispersion
variations comes at a cost of increased band-limited white noise. We discuss
scheduling to minimise this additional noise, and factors, such as
scintillation, that can exacerbate the problem. Comparison with scintillation
measurements confirms previous results that the spectral exponent of electron
density variations in the interstellar medium often appears steeper than
expected. We also find a discrete change in dispersion measure of PSR
J1603-7202 of ~2x10^{-3} cm^{-3}pc for about 250 days. We speculate that this
has a similar origin to the 'extreme scattering events' seen in other sources.
In addition, we find that four pulsars show a wavelength-dependent annual
variation, indicating a persistent gradient of electron density on an au
spatial scale, which has not been reported previously.
