The Differential Microwave Radiometers (DMR) instrument aboard the Cosmic Background Explorer (COBE) has mapped the full microwave sky to mean sensitivity 26 uK per 7 deg field of view. The absolute calibration is determined to 0.7% with drifts smaller than 0.2% per year. We have analyzed both the raw differential data and the pixelized sky maps for evidence of contaminating sources such as solar system foregrounds, instrumental susceptibilities, and artifacts from data recovery and processing. Most systematic effects couple only weakly to the sky maps. The largest uncertainties in the maps result from the instrument susceptibility to the Earth's magnetic field, microwave emission from the Earth, and upper limits to potential effects at the spacecraft spin period. Systematic effects in the maps are small compared to either the noise or the celestial signal: the 95% confidence upper limit for the pixel-pixel rms from all identified systematics is less than 6 uK in the worst channel. A power spectrum analysis of the (A-B)/2 difference maps shows no evidence for additional undetected systematic effects.