  Glitches are sudden increases in the rotation rate $\nu$ of neutron stars,
which are thought to be driven by the neutron superfluid inside the star. The
Vela pulsar presents a comparatively high rate of glitches, with 21 events
reported since observations began in 1968. These are amongst the largest known
glitches (17 of them have sizes $\Delta\nu/\nu\geq10^{-6}$) and exhibit very
similar characteristics. This similarity, combined with the regularity with
which large glitches occur, has turned Vela into an archetype of this type of
glitching behaviour. The properties of its smallest glitches, on the other
hand, are not clearly established. High-cadence observations of the Vela pulsar
were taken between 1981 and 2005 at the Mount Pleasant Radio Observatory. An
automated systematic search was carried out that investigated whether a
significant change of spin frequency $\nu$ and/or the spin-down rate
$\dot{\nu}$ takes place at any given time. We find two new glitches, with
respective sizes $\Delta\nu/\nu$ of $(5.55\pm0.03)\times10^{-9}$ and
$(38\pm4)\times10^{-9}$. In addition to these two glitch events, our study
reveals numerous events of all possible signatures (i.e. combinations of
$\Delta\nu$ and $\Delta\dot{\nu}$ signs), all of them small with
$|\Delta\nu|/\nu<10^{-9}$, which contribute to the Vela timing noise. The Vela
pulsar presents an under-abundance of small glitches compared to many other
glitching pulsars, which appears genuine and not a result of observational
biases. In addition to typical glitches, the smooth spin-down of the pulsar is
also affected by an almost continuous activity that can be partially
characterised by small step-like changes in $\nu$, $\dot{\nu,}$ or both.
Simulations indicate that a continuous wandering of the rotational phase,
following a red spectrum, could mimic such step-like changes in the timing
residuals.
