The Sloan Digital Sky Survey III (SDSS-III) Apache Point Observatory Galactic Evolution Experiment (APOGEE) is a three-year survey that is collecting 105 high-resolution spectra in the near-IR across multiple Galactic populations. To derive stellar parameters and chemical compositions from this massive data set, the APOGEE Stellar Parameters and Chemical Abundances Pipeline (ASPCAP) has been developed. Here, we describe empirical calibrations of stellar parameters presented in the first SDSS-III APOGEE data release (DR10). These calibrations were enabled by observations of 559 stars in 20 globular and open clusters. The cluster observations were supplemented by observations of stars in NASA's Kepler field that have well determined surface gravities from asteroseismic analysis. We discuss the accuracy and precision of the derived stellar parameters, considering especially effective temperature, surface gravity, and metallicity; we also briefly discuss the derived results for the abundances of the α-elements, carbon, and nitrogen. Overall, we find that ASPCAP achieves reasonably accurate results for temperature and metallicity, but suffers from systematic errors in surface gravity. We derive calibration relations that bring the raw ASPCAP results into better agreement with independently determined stellar parameters. The internal scatter of ASPCAP parameters within clusters suggests that metallicities are measured with a precision better than 0.1 dex, effective temperatures better than 150 K, and surface gravities better than 0.2 dex. The understanding provided by the clusters and Kepler giants on the current accuracy and precision will be invaluable for future improvements of the pipeline.