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We present observations of six transits and six eclipses of the transiting planet system HD 189733 taken with the Spitzer Space Telescope's Infrared Array Camera (IRAC) at 8 μm, as well as a re-analysis of previously published data. We use several novel techniques in our data analysis, the most important of which is a new correction for the detector "ramp" variation with a double-exponential function, which performs better and is a better physical model for this detector variation. Our main scientific findings are (1) an upper limit on the variability of the dayside planet flux of 2.7% (68% confidence); (2) the most precise set of transit times measured for a transiting planet, with an average accuracy of 3 s; (3) a lack of transit-timing variations, excluding the presence of second planets in this system above 20% of the mass of Mars in low-order mean-motion resonance at 95% confidence; (4) a confirmation of the planet's phase variation, finding the night side is 64% as bright as the day side, as well as an upper limit on the nightside variability of 17% (68% confidence); (5) a better correction for stellar variability at 8 μm causing the phase function to peak 3.5 hr before secondary eclipse, confirming that the advection and radiation timescales are comparable at the 8 μm photosphere; (6) variation in the depth of transit, which possibly implies variations in the surface brightness of the portion of the star occulted by the planet, posing a fundamental limit on non-simultaneous multi-wavelength transit absorption measurements of planet atmospheres; (7) a measurement of the infrared limb darkening of the star, which is in good agreement with stellar atmosphere models; (8) an offset in the times of secondary eclipse of 69 s, which is mostly accounted for by a 31 s light-travel time delay and 33 s delay due to the shift of ingress and egress by the planet hot spot; this confirms that the phase variation is due to an offset hot spot on the planet; (9) a retraction of the claimed eccentricity of this system due to the offset of secondary eclipse, which is now just an upper limit; and (10) high-precision measurements of the parameters of this system. These results were enabled by the exquisite photometric precision of Spitzer IRAC; for repeat observations the scatter is less than 0.35 mmag over the 590 day timescale of our observations after decorrelating with detector parameters.