  We present new, full-orbit observations of the infrared phase variations of
the canonical hot Jupiter HD 189733b obtained in the 3.6 and 4.5 micron bands
using the Spitzer Space Telescope. When combined with previous phase curve
observations at 8.0 and 24 micron, these data allow us to characterize the
exoplanet's emission spectrum as a function of planetary longitude. We utilize
improved methods for removing the effects of intrapixel sensitivity variations
and accounting for the presence of time-correlated noise in our data. We
measure a phase curve amplitude of 0.1242% +/- 0.0061% in the 3.6 micron band
and 0.0982% +/- 0.0089% in the 4.5 micron band. We find that the times of
minimum and maximum flux occur several hours earlier than predicted for an
atmosphere in radiative equilibrium, consistent with the eastward advection of
gas by an equatorial super-rotating jet. The locations of the flux minima in
our new data differ from our previous observations at 8 micron, and we present
new evidence indicating that the flux minimum observed in the 8 micron is
likely caused by an over-shooting effect in the 8 micron array. We obtain
improved estimates for HD 189733b's dayside planet-star flux ratio of 0.1466%
+/- 0.0040% at 3.6 micron and 0.1787% +/- 0.0038% at 4.5 micron; these are the
most accurate secondary eclipse depths obtained to date for an extrasolar
planet. We compare our new dayside and nightside spectra for HD 189733b to the
predictions of models from Burrows et al. (2008) and Showman et al. (2009). We
find that HD 189733b's 4.5 micron nightside flux is 3.3 sigma smaller than
predicted by the Showman et al. models, which assume that the chemistry is in
local thermal equilibrium. We conclude that this discrepancy is best-explained
by vertical mixing, which should lead to an excess of CO and correspondingly
enhanced 4.5 micron absorption in this region. [abridged]
