  Timing pulses of pulsars has proved to be a most powerful technique useful to
a host of research areas in astronomy and physics. Importantly, the precision
of this timing is not only affected by radiometer noise, but also by intrinsic
pulse shape changes, interstellar medium (ISM) evolution, instrumental
distortions, etc. In this paper we review the known causes of pulse shape
variations and assess their effect on the precision and accuracy of a single
measurement of pulse arrival time with current instrumentation. Throughout this
analysis we use the brightest and most precisely timed millisecond pulsar
(MSP), PSR J0437-4715, as a case study, and develop a set of diagnostic tools
to evaluate profile stability in timing observations. We conclude that most
causes of distortion can be either corrected by state-of-the-art techniques or
taken into account in the estimation of time-of-arrival (TOA) uncertainties.
The advent of a new generation of radio telescopes (e.g. the Square Kilometre
Array, SKA), and their increase in collecting area has sparked speculation
about the timing precision achievable through increases in gain. Based on our
analysis of current data, we predict that for normal-brightness MSPs a TOA
precision of between 80 and 230 ns can be achieved at 1.4 GHz with 10-minute
integrations by the SKA. The actual rms timing residuals for each pulsar will
be approximately at the same level only if all the other influences on timing
precision (e.g. ISM, spin noise) are either corrected, modelled, or negligible.
