Pulsar timing is a technique that exploits the high rotational stability of pulsars, by comparing the average times of arrival (TOAs) of observed pulses with the predictions from a timing model. One of the premier goals in the field of pulsar timing is the direct detection of the stochastic gravitational wave background, through its influence on the TOAs from an ensemble of pulsars. The influence of gravitational waves on pulsar timing data is expected to be very small, and for a detection to be achieved, parameters intrinsic to the pulsar as well as extrinsic factors arising from effects such as propagation through the variable interstellar medium (ISM) must be precisely measured and accounted for. In this thesis, I consider the influence of scattering and dispersion measure (DM) variations, neutron star rotational instabilities, and pulse emission properties on precision pulsar timing measurements. Using 30 years of observations of the Crab Pulsar with Jodrell Bank Observatory's 42-ft telescope at 610 MHz, we have measured the temporal variations in scattering time scales from the influence on observed pulse shapes. Supplementing our 610-MHz data with data taken at 1410 MHz with the Lovell Telescope, we have used multi-frequency TOAs to make precise measurements of the DM variations over a 6-year period. We find that the DM and scattering time scales track each other very closely over this time, with a correlation coefficient of ~0.6. We attribute the variations in DM to discrete high-density regions within the nebula that are of a smaller scale than the 'wisps' seen in optical observations of the nebula, and given the short time scales over which the scattering time scales and DM vary, we estimate the size of these regions to be ~6 AU (equivalent to an angular size of ~2 mas at a distance of 2200 pc). We demonstrate a method of removing the influence of scattering from archival data, by using epoch-specific reference templates that take into account the measured scattering time scales. We find that accounting for the variable scattering time scales leads to a factor of two improvement in root mean square (RMS) timing residuals for the Crab Pulsar. We use TOAs from the European Pulsar Timing Array (EPTA) data release 1.0 (DR1), together with earlier TOAs from the Effelsberg and Lovell Telescopes to show evidence for a deviation from the best-fit timing model. We demonstrate that the deviation from the timing model can be modelled as a glitch in the rotation of the pulsar. We exclude instrumental effects and a gravitational wave burst with memory as potential causes, which may induce similar signals in the residuals. We measure the change in spin-frequency due to the glitch to be âÎ½/Î½=2.5Â±0.1Ã10^(â12) , which is the smallest fractional glitch size reported to date. This is only the second time this phenomenon has been reported in an MSP. We demonstrate that the influence of the glitch can be removed without impacting the timing prospects of the pulsar. We calculate MSP glitch rates and conclude that MSP glitches are rare, and that the probability of another glitch being detected in a timing array pulsar in the next 10 years is ~50%. We measure the DM variations of 31 pulsars that are frequently used as part of pulsar timing arrays, using multi-frequency data sets from DR1 and earlier TOAs recorded with the Lovell Telescope's analogue filterbank. In the best cases, we are able to measure DM variations at a magnitude of âDMâ³10^(â4) cm^(â3) pc. We compare the values we obtain to those published by the North American Nano-Hertz Observatory for Gravitational Waves (NANOGrav) and the Parkes Pulsar Timing Array (PPTA), and find our measured values to be in generally good agreement. Multi-frequency observations made with the Westerbork Synthesis Radio Telescope (WSRT), were particularly well-suited to obtaining precise DM values, and measurements with this instrument were applied to correct the timing residuals of 10 pulsars from our data set, and used to compute structure functions for the DM variations. We find that most pulsars for which we have obtained high-precision measurements of the DM follow a structure function relationship, although for only three out of ten this appears to be consistent with Kolmogorov scaling. We find that in general, the RMS timing residuals of pulsars corrected using a piecewise linear interpolation with our measured DM values are not significantly improved when compared to using DM derivatives to model the variations. We compare the derived timing model parameters from two different DM correction techniques for this subset of our pulsars, and find that the parameters that vary the most between the two techniques are the position and proper motion terms, which vary by >1Ï in most cases. We search for giant pulses (GPs) in observations of PSR B1937+21 made with the Large European Array for Pulsars (LEAP). In 13.4 hrs of observations (equivalent to ~3.1Ã10^(7) rotations), we find 4265 GPs; the largest sample ever gathered for this pulsar. We compare the DM used to optimally-search for GPs to that determined from multi-frequency timing, and find a disagreement between the two techniques. We measure scattering time scales for smoothed GPs, which we find are not correlated with the DM measurements from both of our techniques. We examine the distribution of polarisation fractions of GPs and do not find a correlation between GP flux and fractional polarisation, and find no correlation between polarisation fraction and pulse phase. We calculate the statistics of GP emission rates, and the time intervals between successive GPs, which we use to estimate that a sample size of ~1.5Ã10^(8) rotations is required for a 95% probability of detecting GPs in consecutive rotations. We measure the power law index of the cumulative and non-cumulative flux distributions to be Î±=â3.8Â±0.2 and Î±=â3.44Â±0.08 respectively, and in both cases note a low-flux turnover at ~4 Jy. We measure modulation indices for the GPs, and find that they vary by ~0.5 towards the centre of the pulse phase distributions. We compare the timing prospects of PSR B1937+21 using GPs and the average profile separately, and find no significant improvement in using GPs to time the pulsar, with weighted RMS residuals of ~1.5 Î¼s and ~1.8 Î¼s in the case of the GP TOAs, compared to ~0.7 Î¼s for TOAs from the average profile. In this thesis, I demonstrate that using epoch-specific templates adjusted for observed scattering time scales allows the influence of scattering to be removed from timing residuals. I confirm that glitches occur in MSPs and that their influence on TOAs can be modelled without impacting the timing precision. I show that precision observations at low-frequencies allows the DM variations of pulsars in the EPTA to be monitored and removed from the timing data. I find that, in the case of PSR B1937+21, using GPs to generate TOAs does not lead to a significant improvement in the timing precision of this pulsar.