  We have studied the aperiodic variability of the 401 Hz accreting millisecond
X-ray pulsar SAX J1808.4-3658 using the complete data set collected with the
Rossi X-ray Timing Explorer over 14 years of observation. The source shows a
number of exceptional aperiodic timing phenomena that are observed against a
backdrop of timing properties that show consistent trends in all five observed
outbursts and closely resemble those of other atoll sources. We performed a
detailed study of the enigmatic ~410 Hz QPO, which has only been observed in
SAX J1808.4-3658. We find that it appears only when the upper kHz QPO frequency
is less than the 401 Hz spin frequency. The difference between the ~410 Hz QPO
frequency and the spin frequency follows a similar frequency correlation as the
low frequency power spectral components, suggesting that the ~410 Hz QPO is a
retrograde beat against the spin frequency of a rotational phenomenon in the 9
Hz range. Comparing this 9 Hz beat feature with the Low-Frequency QPO in SAX
J1808.4-3658 and other neutron star sources, we conclude that these two might
be part of the same basic phenomenon. We suggest that they might be caused by
retrograde precession due to a combination of relativistic, classical and
magnetic torques. Additionally we present two new measurements of the lower kHz
QPO, allowing us, for the first time, to measure the frequency evolution of the
twin kHz QPOs in this source. The twin kHz QPOs are seen to move together over
150 Hz, maintaining a centroid frequency separation of $(0.446 \pm 0.009)
\nu_{spin}$.
